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The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities , and to review some problems that remain open. An important… (More)
In this paper we consider the asymptotic stability of a class of discrete-time switching linear systems, where each of the constituent subsystems is Schur stable. We first present an example to motivate our study, which illustrates that the bilinear transform does not preserve the stability of a class of switched linear systems. Consequently, continuous… (More)
Decentralized sequential detection with a fusion center performing the sequential test, " IEEE Trans. Distributed detection of a known signal in dependent gaussian noise, " IEEE Trans. Abstract—In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of… (More)
— Necessary and sufficient conditions for positive realness of general transfer function matrices are derived. These conditions can be checked using eigenvalue solvers for both proper and strictly proper transfer function matrices.
We consider stabilisation of SISO switched linear systems of arbitrary order. Our approach is motivated by applications in which the major design objective is to achieve similar behaviour of the closed-loop system in each mode. We exploit the algebraic properties of a class of matrices to develop design guidelines to achieve this goal for a class of SISO… (More)
In this note we consider the stability properties of a system class that arises in the control design problem of switched linear systems. The control design we are studying is based on a classical pole-placement approach. We analyse the stability of the resulting switched system and develop analytic conditions which reduce the complexity of the stability… (More)
Necessary and sufficient conditions for strict positive realness and positive realness of general transfer function matrices are derived. The conditions are expressed in terms of eigenvalues of matrix functions of the state matrices representation of the LTI system. Illustrative numerical examples are provided.
In this contribution we develop a physical model for a non contact, high-precision Lorentz force planar motion stage of linear DC brushless type. We derive physical models of the relevant components and investigate sources and influences of various parasitic effects and disturbances. For the latter, phenomenological models are developed that capture the… (More)