Peter Moylan

University of Newcastle Australia · Department of Electrical Engineering

We introduce the concept of "consistently negative feedback" (CNF) in a control system. This is a generalisation of the property of a linear system where the feedback is negative at all frequencies. A number of properties of CNF systems are derived.

Shows how to formulate Kirchoff's laws as a feedback between outputs and inputs.

Earlier results on algebraic criteria for dissipative systems are extended to a wider class of supply rates which do not have to be quadratic in the state.

Some results in dissipative systems theory require that the supply rate be such that it can be forced negative by choice of input. In this note we show that this can be expressed as an eigenvalue condition.

This report deals with the problem of designing and implementing digital filters in software. The report is, in effect, documentation for the accompanying software.

Standard algorithms for QR decomposition assume that the matrix in question has full rank. We present an alternative that can, without pivoting, handle the rank-deficient case, and that produces an í µí±¹ matrix that has linearly independent rows. One application of this approach is the efficient calculation of pseudoinverses.

A system is dissipative if it satisfies a special iAnequality relating the system input and output. (Passivity, for example, is a special case of dissipativeness.) The use of the dissipativeness concept includes things like testing interconnected systems for stability. This relies, however, on having practical (and preferably simple) ways of testin...

An overview of the theory of dissipative dynamical systems, and some stability results that come from that theory.

This paper addresses a multi-level threshold strategy for buffer space management in ATM networks. We consider a buffer of finite capacity loaded with a number of on-off sources. Each source generates two types of cells, high priority cells and low priority cells. An arriving cell of low priority will be rejected if the buffer content at the cell a...

A state dependent cost of accepting a call is introduced to measure the benefit of alternate routes. This cost function, which requires expensive calculations, can be approximated to a linear form without much error. Based on this cost approximation, a dynamic trunk reservation level is derived. It is easy to implement on-line and gives a better ov...

To control the performance of a packet-switched network efficiently, some knowledge on dynamic behavior of the network needs to be investigated. In this paper, we apply an adaptive control technique, recursive least square (RLS) estimation, to propose a new approach to estimating the traffic parameters of the network. Based on an introduced dynamic...

In software systems using preemptive scheduling based on task priorities, it is desirable to include a priority inheritance mechanism. This is an arrangement by which a task's priority is temporarily increased when it is blocking a task of higher priority. Although it is easy to work out when and how to increase a task's priority, the subsequent re...

This note extends the results of the existing dissipative systems theory to include locally dissipative systems. This extension enables us to analyze an interconnection of locally dissipative systems. The dissipative systems theory has been successful in unifying the input-output analysis and the state-space analysis; so far, a ''local'' version of...

This paper discusses a number of practical issues related to the software environment required for the successful implementation of medium to large scale control systems. It is argued that for all but trival systems it is desirable to implement the control system within a software environment which formally supports real-time multi-tasking.

PMOS is an “operating system” which has been under development by the author for the last several years. The description “operating system” is only partly appropriate since a decision was made at the outset not to concentrate on the conventional user-level features such as a command decoder, program development tools, program loaders, and the like....

A Lyapunov function is constructed for a general n -machine power system with nonzero transfer conductance. The theory of dissipative dynamic systems and its modifications are used. The Lyapunov function construction procedure calls for checking positive definiteness of a sparse matrix. Results are reported only for the case of nonuniform damping,...

This paper discusses a number of practical issues related to the software environment required for the successful implementation of medium to large scale control systems. It is argued that for all but trival systems it is desirable to implement the control system within a software environment which formally supports real-time multi-tasking.

PMOS is an “operating system” which has been under development by the author for the last several years. The description “operating system” is only partly appropriate since a decision was made at the outset not to concentrate on the conventional user-level features such as a command decoder, program development tools, program loaders, and the like....

For network management functions such as the decision on whether to accept or block an incoming call request, it is desirable to have some form of short-term prediction of the traffic levels in the network. The form that a predictor should take is not obvious. We introduce a new quantity called the Expected Mean Demand (EMD), which is a measure of...

A method is given for deriving a Lyapunov function for a two-machine power system with nonzero transfer conductances. The assumptions required are only mildly restrictive and are likely to be satisfied for practical values of machine parameters. The method shows promise for extension to systems of more than two machines.

General results giving conditions for an interconnected system to be input-output and/or Lyapunov unstable are considered. These results are derived in terms of the theory of dissipative systems. This enables a very simple formulation of the requirements for instability. In particular, the restrictions linearity and unstable subsystems, that appear...

Passivity is perhaps the most basic concept in circuit theory. Unfortunately, the existing definitions of passivity are too restrictive and often contradict one another. In this paper, a new passivity definition is proposed which is applicable to all n-port and (n + 1)-terminal devices—including time-varying, non-linear, and distributed circuit ele...

A recently published stability criterion allows checking the stability of a large-scale system whose subsystems are dissipative. (Dissipativeness is a property, akin to, but more general than, passivity.) The criterion requires that a certain test matrix be positive definite. It is now shown that one can sometimes deduce stability when the test mat...

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The relationship between input-output and Lyapunov stability properties for nonlinear systems is studied. Well-known definitions for the input-output properties of finite-gain and passivity, even with quite reasonable minimality assumptions on a state-space representation, do not necessarily imply any form of stability for the state. Attention is g...

When a large scale system is formed from linear interconnections of a number of passive subsystems, a diagonal dominance condition on the interconnection matrix is known to ensure asymptotic stability. It is shown that the same condition ensures that stability is retained when a large class of nonlinearities, including nonlinearities with memory, i...

A complete account is given of the theory of so-called dissipative dynamical systems. The concept of dissipativeness is defined as a general input-output property which includes, as notable special cases, passivity and other properties related to finite-gain. The aim is to treat input-output and state properties side-by-side with emphasis on explor...

This paper describes simple sufficient conditions for stability and instability of interconnected systems in terms of the properties of the subsystems and of the interconnections. The central theme is the notion of "dissipativeness" of the subsystems-a property which includes finite gain, passivity, conicity, and some other variants as special case...

A description is given of simple sufficient conditions for stability and instability of interconnected systems in terms of the properties of the subsystems and of the interconnections. The central theme is the notion of ″dissipativeness″ of the subsystems - a property which includes finite gain, passivity, conicity, and some other variants as speci...

A general result giving conditions for a feedback system to be input-output unstable is considered. The result is derived in terms of a theory of dissipative systems, which enables a very simple formulation of the requirements for instability. A wide variety of useful instability criteria can be easily obtained as special cases.

Recent research into large-scale system stability has proceeded via two apparently unrelated approaches. For Lyapunov stability, it is assumed that the system can be broken down into a number of subsystems, and that for each subsystem one can find a Lyapunov function (or something akin to a Lyapunov function). The alternative approach is an input-o...

A new necessary and sufficient condition is given for all principal minors of a square matrix to be positive. A special subclass of such matrices, called quasidominant matrices, is also examined.

This paper presents an approach towards deriving sufficient conditions for the stability of nonlinear feedback systems. The central features of the approach are twofold. Firstly, useful stability tests are obtained for the case when the subsystems have nonlinear dynamics; secondly, a unifying set of general stability criteria are given, from which...

A new and computationally efficient algorithm for inversion of linear time-invariant systems is presented. Existence conditions for either left- or right-inverse systems are also presented together with stability criteria. These criteria indicate that the algorithm will find a stable inverse whenever one exists. The results apply to both left and r...

The existence of a solution to a linear-quadratic singular control problem is equivalent to the existence of a solution to a certain matrix inequality. This paper studies an approach to solving the inequality, and identifies the maximal solution of the inequality as defining the performance index infimum for the control problem.

A method is described for generating Lyapunov functions for multi machine power systems. It is based on recent work on stability tests for interconnected dissipative control systems.

A method is described for generating Lyapunov functions for multi machine power systems. It is based on recent work on stability tests for interconnected dissipative control systems.

Abstract--This short paper presents a technique for generating Lyapunov functions for a broad class of nonlinear systems represented by state equations. The system, for which a Lyapunov function is required, is assumed to have a property called dissipativeness. Roughly speaking, this means that the system absorbs more energy from the external world...

A simple frequency domain inequality is known to be necessary but not, in general, sufficient, for the existence of the infimum defined by a linear-quadratic optimal control problem. This note shows that for a certain class of performance indices, the condition is also sufficient.

A new and computationally efficient algorithm for inversion of linear time-invariant systems is presented. Existence conditions for either left or right inversions are presented, together with stability criteria. These criteria indicate that the algorithm will find a stable inverse if one exists. The results apply to both left and right inverses.

The development of synthesis procedures for passing from a prescribed rational positive real function or matrix to a linear lumped network of passive components possessing the prescribed quantity as its impedance has been one of the major problems confronting network theorists in the past. One of the earliest such synthesis procedures is the O. Bru...

For a given nonstationary matrix covariance with a finite-dimensionality property that is the time-varying generalization of the rational power spectrum matrix property, we show how to find a linear finite-dimensional system driven by white noise with output covariance equal to the prescribed covariance.

A state-space synthesis procedure is given for linear timevarying passive impedance matrices. The synthesis uses only passive components.

Excitation control of a synchronous generator is discussed. Linear systems theory is used to derive a simple feedback formula.

For a broad class of nonlinear systems, a connection is established between the input-output property of passivity and a set of constraints on the state equations of the system. These constraints are then interpreted in terms of the stored energy and dissipation of a passive system. Applications are given in two problems of optimal control theory,...

The limiting form of the Kalman-Bucy filter as measurement noise tends to zero does not, in general, correspond to the optimal filter derived assuming zero measurement noise. This may be considered to be due to a difference in initial conditions.

State-space techniques for impedance matrix synthesis can be difficult to apply when the prescribed impedance matrix Z(s) is such that Z(infty) + Z'(infty) is singular. Here this problem is overcome by a sequence of preliminary lossless extractions. In the case of lossless networks, the procedure reduces to a multiport Cauer synthesis.

Nonlinear optimal regulators are discussed, and some useful properties are isolated. An inverse problem of nonlinear regulator design is posed and solved.

This paper considers a new approach to the optimization of the linear, possibly time-varying, system x ̇ = Fx + Gu |ui| ≤ 1 with respect to the performance index V = ∫t1t0x′Qxdt. The new approach applies standard regulator theory using appropriate transformations and thereby enables the problem to be solved more completely than has hitherto been po...

Nonlinear optimal regulators are discussed, and some useful properties are isolated. An inverse problem of nonlinear regulator design is posed and solved.

It is shown that a nominally linear system with relay feedback is insensitive to unintentional time-variable gains or non-linearities in the input transducers when the relay is chattering.

The problem of minimising ¿t0¿(x¿Qx + u¿Ru)dt for a completely controllable linear system, subject to the constraint |u¿|< 1, is shown to be equivalent to a singular optimal-control problem; the known singular theory is then used to obtain the optimal control.