# Alberto TesiUniversity of Florence | UNIFI · Dipartimento di Ingegneria dell'Informazione

Alberto Tesi

Professor

## About

242

Publications

12,052

Reads

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6,430

Citations

## Publications

Publications (242)

In the last few years the literature has witnessed a remarkable surge of interest for maps implemented by discrete-time (DT) memristor circuits. This paper investigates on the reasons underlying this type of complex behavior. To this end, the papers considers the map implemented by the simplest memristor circuit given by a capacitor and an ideal fl...

Discretization schemes such as Euler method and Runge–Kutta techniques are extensively used to find approximate solutions of Continuous-Time (CT) dynamical system. While the approximation is good for small discretization step sizes, as pointed out by Lorenz, when the step size increases, computational chaos and computational instability are frequen...

In the last decade the flux-charge analysis method (FCAM) has been successfully used to show that continuous-time (CT) memristor circuits possess for structural reasons first integrals (invariants of motion) and their state space can be foliated in invariant manifolds. Consequently, they display an initial condition dependent dynamics, extreme mult...

In the last decade the flux-charge analysis method (FCAM) has been successfully used to show that continuous-time (CT) memristor circuits possess for structural reasons first integrals (invariants of motion) and their state space can be foliated in invariant manifolds. Consequently, they display an initial condition dependent dynamics, extreme mult...

The use of ideal memristors in a continuous-time (CT) nonlinear circuit is known to greatly enrich the dynamic behavior with respect to the memristorless counterpart, which is a crucial property for applications in future analog electronic circuits. This can be explained via the flux–charge analysis method (FCAM), according to which CT circuits wit...

Nonvolatile memristive devices display nonlinear characteristics suitable for implementing circuits exhibiting oscillations or more complex dynamic behaviors, including chaos. However, the results presented in related works are mostly limited to simulations and employing ideal memristor models whose resistance is governed by a charge-flux relation...

The article shows that transient chaos phenomena can be observed in a generalized memristor Chua's circuit where a nonlinear resistor is introduced to better model the real memristor behaviour. The flux‐charge analysis method is used to explain the origin of transient chaos, that is attributed to the drift of the index of the memristor circuit inva...

Although Lyapunov exponents have been widely used to characterize the dynamics of nonlinear systems, few methods are available so far to obtain a priori bounds on their magnitudes. Recently, sufficient conditions to rule out the existence of attractors with positive Lyapunov exponents have been derived via a Lyapunov approach based on the second ad...

The paper considers a class of discrete-time cellular neural networks (DT-CNNs) obtained by applying Euler’s discretization scheme to standard CNNs. Let T be the DT-CNN interconnection matrix which is defined by the feedback cloning template. The paper shows that a DT-CNN is convergent, i.e. each solution tends to an equilibrium point, when T is sy...

Nonlinearity is a central feature in demanding computing applications that aim to deal with tasks such as optimization or classification. Furthermore, the consensus is that nonlinearity should not be only exploited at the algorithm level, but also at the physical level by finding devices that incorporate desired nonlinear features to physically imp...

The article considers a large class of delayed neural networks (NNs) with extended memristors obeying the Stanford model. This is a widely used and popular model that accurately describes the switching dynamics of real nonvolatile memristor devices implemented in nanotechnology. The article studies via the Lyapunov method complete stability (CS), i...

This paper introduces a small-gain sufficient condition for $2$-contraction of feedback interconnected systems, on the basis of individual gains of suitable subsystems arising from a modular decomposition of the second additive compound equation. The condition applies even to cases when individual subsystems might fail to be contractive (due to the...

Oscillatory circuits with real memristors have attracted a lot of interest in recent years. The vast majority of circuits involve volatile memristors, while less explored is the use of non-volatile ones. This paper considers a circuit composed by the interconnection of a two-terminal (one port) element, based on the linear part of Chua’s circuit, a...

A well-known feature of memristors is that they makes the circuit dynamics much richer than that generated by classical
RLC
circuits containing nonlinear resistors. In the case of circuits with ideal memristors, such a multistability property, i.e., the coexistence of many different attractors for a fixed set of parameters, is connected to the fa...

The paper considers a neural network with a class of real extended memristors obtained via the parallel connection of an ideal memristor and a nonlinear resistor. The resistor has the same rectifying characteristic for the current as that used in relevant models in the literature to account for diode-like effects at the interface between the memris...

Nonlinearity is a central feature in demanding computing applications that aim to deal with tasks such as optimization or classification. Furthermore, the consensus is that nonlinearity should not be only exploited at the algorithm level, but also at the physical level by finding devices that incorporate desired nonlinear features to physically imp...

Neural networks with memristors are promising candidates to overcome the limitations of traditional von Neumann machines via the implementation of novel analog and parallel computation schemes based on the in-memory computing principle. Of special importance are neural networks with generic or extended memristor models that are suited to accurately...

The paper deals with Limit Cycle Oscillations (LCOs) in a Pitch & Plunge model of the wing dynamics, where the stiffness on the plunge displacement is assumed to be an odd fifth-order polynomial. First, it is shown that the model dynamics can be equivalently described via a Lur’e system, i.e., the feedback interconnection between a linear time-inva...

The paper considers a wide class of circuits containing memristors, coupled and nonlinear capacitors and inductors, linear resistive multi-ports and independent voltage and current sources. A new method is proposed to analyze the invariants of motion and invariant manifolds of memristor circuits in this class. The method permits to show the existen...

Stanford memristor model is a widely used model that accurately characterizes real non-volatile metal-oxide resistive random access memory (RRAM) devices with bipolar switching characteristics. The paper studies for the first time the dynamics and bifurcations in a class of nonlinear oscillators with
real non-volatile memristor devices
obeying St...

Second additive compound matrices of the system’s Jacobian are used to formulate sufficient conditions to rule out existence of attractors with positive Lyapunov exponents. The criteria are expressed in terms of Lyapunov dissipation inequalities or Linear Matrix Inequalities amenable to analytic verification. The results extend applicability of pre...

The chapter reviews a recently proposed input–output approach to investigate the dynamics of a class of circuits composed of a linear time-invariant two-terminal element coupled with one ideal flux-controlled memristor. The classical (autonomous) Chua’s and (non-autonomous) Murali–Lakshmanan–Chua’s memristor circuits are employed to discuss the fea...

Random mechanisms including mutations are an internal part of evolutionary algorithms, which are based on the fundamental ideas of Darwin’s theory of evolution as well as Mendel’s theory of genetic heritage. In this paper, we debate whether pseudo-random processes are needed for evolutionary algorithms or whether deterministic chaos, which is not a...

The paper considers the problem of controlling multistability in a general class of circuits composed of a linear time-invariant two-terminal (one port) element, containing linear R , L , C components and ideal operational amplifiers, coupled with one of the mem-elements (memory elements) introduced by Prof. L.O. Chua, i.e., memristors, memcapacito...

Since the introduction of memristors, it has been widely recognized that they can be successfully employed as synapses in neuromorphic circuits. This paper focuses on showing that memristor circuits can be also used for mimicking some features of the dynamics exhibited by neurons in response to an external stimulus. The proposed approach relies on...

The paper proposes a novel input–output approach to characterize the dynamical properties of a class of circuits composed by a linear time-invariant two-terminal element coupled with one of the ideal memelements (memory elements) introduced by Prof. L. O. Chua, i.e. memristors, memcapacitors, and meminductors. The developed approach permits to read...

This article introduces a new class of memristor neural networks (NNs) for solving, in real-time, quadratic programming (QP) and linear programming (LP) problems. The networks, which are called memristor programming NNs (MPNNs), use a set of filamentary-type memristors with sharp memristance transitions for constraint satisfaction and an additional...

The paper studies bifurcations and complex dynamics in a class of nonautonomous oscillatory circuits with a flux-controlled memristor and harmonic forcing term. It is first shown that, as in the autonomous case, the state space of any memristor circuit of the class can be decomposed in invariant manifolds. It turns out that the memristor circuit dy...

The paper studies nonlinear dynamics and bifurcations of a class of memristor oscillatory circuits obtained by replacing the nonlinear resistor of a Chua's oscillator with a flux-controlled memristor. A recently developed technique, named flux-charge analysis method, has shown that the state space of such circuits can be decomposed in invariant man...

This note deals with the problem of controlling an uncertain discrete-time linear system by means of a hybrid controller in the form of a linear system whose parameters switch among a finite number of possible configurations, called modes. We suppose that each single controller is designed in order to individually ensure robust stability for a dual...

In this paper, a novel adaptive disturbance attenuation algorithm is proposed combining switching and tuning. A two-level hierarchical switching logic is developed, which first selects in a short time the potentially best controller among a finite pre-designed family and then performs a local refinement of its attenuation capability. Thanks to the...

In this paper, a new algorithm is proposed for the design of a family of controllers to be used within an adaptive switching control scheme. The resulting switching controller is able to attenuate the effects of disturbances having uncertain and possibly time-varying characteristics, as well as to ensure stability under arbitrary switching sequence...

The paper discusses the application of two recently proposed feedback control techniques for stabilizing chaotic motions to periodic ones in a CO 2 laser with modulated losses. The first method employs delayed control signals for stabilizing unstable periodic orbits embedded in the chaotic attractor, while the second one is based on the cancellatio...

In this paper, an algorithm combining switching and tuning is proposed as a solution to the problem of adaptive disturbance attenuation. A high-level switching logic selects the controller providing the best potential performance within a pre-designed family; then a tuning procedure aims at finding a local refinement of the selected controller in o...

The problem of adaptive disturbance attenuation is addressed in this paper using a switching control approach. A finite family of stabilizing controllers is pre-designed, with the assumption that, for any possible operating condition, at least one controller is able to achieve a prescribed level of attenuation. Then, at each time instant, a supervi...

The problem of reducing the effects of wavefront distortion and
structural vibrations inground-based telescopes is addressed within a
modal-control framework. The proposed approach aimsat optimizing the
parameters of a given modal stabilizing controller with respect to a
performance criterionwhich reflects the residual phase variance and is
defined...

The problem of reducing the effects of wavefront distortion and structural vibrations in
ground-based telescopes is addressed within a modal-control framework. The proposed approach aims
at optimizing the parameters of a given modal stabilizing controller with respect to a performance criterion
which reflects the residual phase variance and is defi...

Saluto di benvenuto del Rettore dell'Università degli Studi di Firenze al Seminario internazionale di studi "Global Interoperability and Linked Data in Libraries".

This paper addresses the problem of reducing the effects of wavefront distortions in ground-based telescopes within a “Modal-Control” framework. The proposed approach allows the designer to optimize the Youla parameter of a given modal controller with respect to a relevant adaptive optics performance criterion defined on a “sampled” frequency domai...

In this paper the problem of local exponential stability of periodic orbits in a general class of forced nonlinear systems is considered. Some lower bounds for the degree of local exponential stability of a given periodic solution are provided by mixing results concerning the analysis of linear time-varying systems and the real parametric stability...

When the neuron interconnection matrix is symmetric, the standard Cellular Neural Networks (CNN's) introduced by Chua and Yang [1988a] are known to be completely stable, that is, each trajectory converges towards some stationary state. In this paper it is shown that the interconnection symmetry, though ensuring complete stability, is not in the gen...

The paper presents a new approach to the control of chaotic systems for the stabilization of a periodic orbit. The problem formulation requires preserving a number of original system characteristics and making use of a low energy control. The proposed method follows a frequency harmonic balance technique employed in the approximate analysis of comp...

The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order m...

The paper deals with the characterization of Hopf bifurcations in families of third order autonomous systems involving quadratic nonlinearities. By employing Harmonic Balance (HB) tools, the set of system parameters corresponding to supercritical and subcritical bifurcations is analytically determined, together with an approximation of the actual b...

This chapter addresses robustness analysis of polytopic systems affected by time-varying uncertainties with known bounds on
their variation rate. The analysis is conducted by introducing the class of HPD-HLFs, i.e. Lyapunov functions that are forms
in both the state and the uncertain parameters, which includes the classes of HPLFs and HPD-QLFs as s...

Chapter 3 has investigated robust stability and performance of systems with time-varying uncertainties. Another class of fundamental problems in systems engineering concerns robustness analysis of systems affected by time-invariant uncertainties. Such problems arise, for example, when one has to establish whether all systems contained in a given se...

This chapter addresses robust stability of time-varying systems affected by structured parametric uncertainty, a fundamental
problem in robust control. It is shown that the problem can be tackled by employing Lyapunov functions which are forms in
the state variables and are referred as HPLFs. Thanks to the tools for checking positivity of forms int...

This chapter presents further results for robustness analysis of uncertain systems based on forms. It is shown how the problem
of computing the euclidean distance from a point to a surface described by a polynomial equation, can be solved via LMI feasibility
tests. This problem has numerous applications in systems and control theory. In this respec...

This chapter addresses the problem of studying positivity of a form, i.e. a polynomial whose terms have all the same degree. This is a key issue which has many implications in systems and control
theory. A basic tool for the representation of forms, which is known in the literature as Gram matrix or SMR, is introduced.
The main idea is to represent...

This chapter investigates the gap between positive forms and SOS forms. Conservatism of the LMI relaxations described in Chapter
1 is related to the existence of positive forms which are not SOS, called PNS forms. a priori conditions for non-conservatism of these relaxations are presented for some classes of forms. The class of SMR-tight forms
is i...

Positive Forms.- Positivity Gap.- Robustness with Time-varying Uncertainty.- Robustness with Time-invariant Uncertainty.- Robustness with Bounded-rate Time-varying Uncertainty.- Distance Problems with Applications to Robust Control.

In this paper, the dynamical behavior of a class of third-order competitive cellular neural networks (CNNs) depending on two parameters, is studied. The class contains a one-parameter family of symmetric CNNs, which are known to be completely stable. The main result is that it is a generic property within the family of symmetric CNNs that complete...

The symmetry of the neuron interconnection matrix ensures that additive neural networks are completely stable, i.e., each
trajectory converges towards some equilibrium point. However, the crucial point is that in any practical realization it is
not possible to implement perfectly symmetric interconnections, and therefore robustness of complete stab...

The paper investigates Hopf bifurcations in a class of simple nonlinear systems, i.e., third order affine control systems described in terms of "quadratic plus cubic" normal forms and subject to linear state feedback control laws. By employing Harmonic Balance (HB) tools, the set of system parameters corresponding to supercritical and subcritical b...

This paper considers the problem of determining the minimum euclidean distance of a point from a polynomial surface in R
n. It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent
Linear Matrix Inequality (LMI) techniques can be exploited for solving this problem. The first result...

In this note the problem of restricted complexity stability margin maximization (RCSMM) for single-input-single-output (SISO) plants affected by rank one real perturbations is considered. This problem amounts to maximizing the real l<sub>2</sub> parametric stability margin over an assigned class of restricted complexity controllers, which are descr...

This paper deals with robust stability analysis of linear state space systems affected by time-varying uncertainties with bounded variation rate. A new class of parameter-dependent Lyapunov functions is introduced, whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogene...

Cellular neural networks (CNNs) are one of the most popular paradigms for real-time information processing. Recently, CNNs have found interesting applications in the solution of on-line optimization problems, and the implementation of intelligent sensors. In these applications the CNNs are required to be completely stable, i.e. each trajectory shou...

In the sixties, Łojasiewicz proved a fundamental inequality for vector fields defined by the gradient of an analytic function, which gives a lower bound on the norm of the gradient in a neighborhood of a (possibly) non-isolated critical point. The inequality involves a number belonging to (0, 1), which depends on the critical point, and is known as...

The paper deals with the characterization of Hopf bifurcations in families of simple nonlinear systems, i.e., third-order autonomous systems with few nonlinear terms. By employing Harmonic Balance (HB) tools, the complete set of system parameters corresponding to supercritical and subcritical bifurcations is determined. In addition, it is shown how...

Robust stability analysis of state space models with respect to real parametric uncertainty is a widely studied challenging problem. In this paper, a quite general uncertainty model is considered, which allows one to consider polynomial nonlinearities in the uncertain parameters. A class of parameter-dependent Lyapunov functions is used to establis...

This paper deals with a central issue in bifurcations and chaos control applications, i.e., the stabilization of periodic motions in sinusoidally forced nonlinear systems. Specifically, the problem of designing multi-input–multi-output (MIMO) finite-dimensional linear time-invariant controllers maximizing the amplitude of the sinusoidal input for w...

In this note, robust stability of state-space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the homogeneous polynomially parameter-dependent quadratic Lyapunov functions (HPD-QLF...

In this paper robust stability of linear state space models with respect to time-varying uncertainties with bounded variation rates is considered. A new class of parameter-dependent Lyapunov functions to establish stability of a polytope of matrices in presence of a polytopic bound on the variation rate of the uncertain parameters is introduced, i....

The problem of estimating the domain of attraction (DA) of equilibria is considered for odd polynomial systems. Specifically, the computation of the optimal quadratic Lyapunov function (OQLF), i.e. the quadratic Lyapunov function (QLF) which maximizes the volume of the largest estimate of the DA (LEDA), is addressed. In order to tackle this double...

The computation of robust H ∞ performance of linear systems subject to polytopic parametric uncertainty is known to be a difficult problem in robust control. In this paper, quadratic parameter-dependent Lyapunov functions, with polynomial dependence on the uncertain parameters, are exploited to provide upper bounds to the robust H ∞ performance. It...