# Chaker JammaziÉcole Nationale d'Ingénieurs de Tunis, and Ecole Polytechnique de Tunisie · Laboratoire d'Ingénierie Mathématique (LIM)

Chaker Jammazi

HdR

## About

44

Publications

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318

Citations

Introduction

## Publications

Publications (44)

This paper considers the stabilization problem of bilinear systems in small time by
various feedback laws. Then, under some reasonable assumptions on the system and control operator, we prove the global polynomial stabilization of the bilinear system, at hand, in a small time by unbounded feedback. A decay rate of the stabilized state is explicitly...

This paper studies a class of inertial neural networks with leakages and varying delays on timescales: xi△△(t)=-ai(t)xi△(t-ηi(t))-bi(t)xi(t-ξi(t))+∑j=1ncij(t)fj(xj(t))+∑j=1ndij(t)gj(xj(t-qij(t)))+Si(t).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{m...

We prove in this paper the global approximate controllability of the 1-D Boussinesq equation-subjected to internal control and free boundary conditions-on a bounded domain. The key ingredients of the proof relies Coron's return method for the exact global controllability of the nonlinear control system \begin{document}$ y_{tt}+(y^2)_{xx} = u(t) $\e...

New investigations in the problems of polynomial stabilization are presented in this paper, where some relaxed results related to homogeneity theory leading to this polynomial stability with optimal decay rate are developed. To achieve our analysis, several physical examples are presented showing how we can construct stabilizing feedback laws makin...

This paper discusses the finite-time stabilization of some linear hyperbolic partial differential equations by persistently exciting boundary feedbacks. The construction of stabilizing feedbacks is based on Lyapunov approach. A particular attention is paid to transport and wave control systems. The obtained results are used to solve two problems: t...

In this paper, the problem of internal finite‐time stabilization for 1‐D coupled wave equations with interior point mass is handled. The nonlinear stabilizing feedback law leads, in closed‐loop, to nonlinear evolution equations where Kato theory is used to prove the well‐posedness. In addition, it is showed that in some cases, the solution of this...

In this paper, the problem of global finite-time stabilization of bilinear control systems by means of homogeneous feedback law is investigated. We prove under some reasonable assumptions on the operators A and B that continuous bounded and discontinuous unbounded feedbacks stabilize globally in finite-time the closed loop system. For illustrative,...

This paper presents new criteria for the rational stability of dynamical systems. We introduce basic and useful results on how to construct control laws to assure rational stability. Both Coron and Sontag examples were re-visited. A particular attention is paid to time-varying systems where sufficient Lyapunov conditions are developed guaranteeing...

This paper introduces a new approach to ensure the decentralized horizon suboptimal control of interconnected nonlinear systems based on the decentralized finite-state-dependent Riccati equation. This approach is, in fact, a new extension of the state-dependent Riccati equation technique with a finite horizon for the case of large-scale nonlinear s...

Abstract: In this article, the problem of finite-time stabilization of two strings connected by point mass is discussed. We use the so-called Riemann coordinates to convert the study system into four transport equations coupled with the dynamic of the charge. We act by Bhat-Bernstein feedbacks in various positions (two extremities, the point mass a...

This paper presents the finite time stabilisation strategy of two problems: the first one is the control of the high voltage direct current based on voltage source converter, while the second is the control of the multi-terminal direct current transmission systems. Subject to finite-time control design strategy, a linear and nonlinear dynamic model...

This paper deals with the problem of rational stabilizability of nonlinear control systems by optimal control. Many sufficient conditions are derived characterizing the partial rational stabilizability by optimal feedback laws. Our main results are applied on the class of control systems with drift, where an optimal feedback laws are built stabiliz...

This article presents a backstepping control design strategy for the voltage source converter (VSC)-based high-voltage direct current (HVDC). First, a dynamic model is derived based on the state space description. Subject to the backstepping control design procedure strategy, a non-linear control scheme is developed in the sense of Lyapunov stabili...

This article deals with an extension of several sufficient conditions for finite-time stability with application to triangular control systems. These results are applied to some classical problems like the three-wheeled vehicle, the angular momentum equation of satellite, the attitude of the drone X4
and the satellite with moving masses

This paper deals with the finite-time stabilizability of some hyperbolic systems by various feedbacks. We have shown under a finite-time boundary feedback laws, that a class of hyperbolic systems is finite-time stabilizable. The idea of this stabilization is based on “ strict minimal ” feedback laws and exploit the switching boundary conditions. Fi...

This article proves that if the linearized control system is controllable, then the nonlinear control system can be locally stabilized in finite-time by means of continuous or even by discontinuous state feedback laws. We applied the main result for the construction of stabilizing feedbacks making the partial guidance in finite-time of some space a...

In this paper, the problem of rational stabilizability of nonlinear control system by optimal feedback laws is considered. By using Hamilton-Jacobi-Belleman approach, some sufficient conditions are derived characterizing the rational stabilizability by optimal control for every dynamical control systems. As application, we have treated the example...

In this paper, the problem of finite-time boundary stabilization of two strings
connected by point mass is investigated. Based on the so-called Riemann invariant transformation, the vibrating strings are
transformed in two hybrid-hyperbolic systems, and leads to the posedness of our system. In order to act in the
system, it is desirable to choose b...

In this paper an extension of several sufficient conditions for finite-time stability of triangular systems are provided. We apply our conditions to show that the angular momentum equations, for a rigid spacecraft with two controls, is finite-time stabilizable. This allows to conclude the partial guidance of several under-actuated systems as the X4...

In this paper, we study the finite-time consensus problem of networked nonlinear systems under directed fixed graph. A nonlinear system is considered as a controlled first-order differential equation with/without drift term commonly used to model autonomous systems. For multi-system formation under directed fixed graph, a protocol is proposed to so...

This paper gives various constructions of stabilizing feedbacks of the well-known chained systems by various approaches. Briefly, the paper presents new alternatives to overcome the Brockett’s obstruction; these alternatives are the finite-time partially stabilizability by continuous or discontinuous state feedback laws.

In this paper, we give a construction of discontinuous feedback laws stabilizing in finite-time all without drift systems. Our construction is based on “sampling control” defined by Clarke et al. [6] and on Bhat and Bernstein feedback laws for cascaded structures [3]. Moreover, our construction are extended to another family of systems as satellite...

In this paper, several sufficient conditions for rational stability are provided. We applied our conditions to show that all chained systems are rationally stabilized-by Hölderian feedback laws – in partial sense. In addition, we show that the backstepping techniques can be extended to rational stabilizability theory.

In this paper, the problem of partial asymptotic stabilization of the nonlinear autonomous under actuated airship (AUA) by various feedback laws is investigated. It has been shown that the AUA's is not stabilizable via continuous pure-state feedback. This is due to (Brockett 1983), necessary condition. In order to cope with this difficulty, we prop...

We consider chained systems that model various systems of mechanical or biological
origin. It is known according to Brockett that this class of systems, which are
controllable, is not stabilizable by continuous stationary feedback (i.e.
independent of time). Various approaches have been proposed to remedy this
problem, especially instationary or di...

The article gives Lyapunov-type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero, while the rest converge to constant values that possibly depend on the initial conditions. The article then presents partially asymptotically stabilizing controllers for many non-linear control syste...

The paper gives Lyapunov type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for...

In this paper, the problem of partial asymptotic stabilization of nonlinear control cascaded systems with integrators is considered. Unfortunately, many controllable control systems present an anomaly, which is the non complete stabilization via continuous pure-state feedback. This is due to Brockett necessary condition. In order to cope with this...

The Note deals with partial stabilization in finite-time of a class of nonlinear chained systems. It is well known that the chain of integrators of length n is not asymptotic stabilizable by continuous stationary feedback laws. This follows from the Brockett necessary condition for stabilizability. To overcome this limitation, we construct feedback...

This paper studies the partial asymptotic stabilization of underactuated axi‐symmetric rigid spacecraft with two controllers. We have shown that axi‐symmetric rigid spacecraft is not controllable, and cannot be asymptotically stabilizable by continuous pure state feedback laws. In order to overcome these limitations we treat the stabilization probl...

In this work, the problem of partial stabilization of nonlinear control cascade systems with integrators is considered. The latter systems present an anomaly, which is the non complete stabilization via continuous purestate feedback, this is due to Brockett necessary condition. To cope with this difficulty we propose the partial stabilization. For...

This paper addresses the concept of partial stabilization for driftless control systems called "nonholonomic systems". We introduce a class of feedback transformations that transforms our system in to a multi-chained triangular form. We show that we can bounded the first component; this can be done by using a smooth feedback control depending on th...

This paper deals with a stability theory for constrained dynamic systems which are defined as dynamic systems whose state trajectories are restricted to a particular set within the state space called the constrained manifold. The constrained dynamic systems considered here are a mechanical system with holonomic constraints, which can be modeled by...