Root-mean-square gains of switched linear systems: A variational approach (original) (raw)
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This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence.
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Stability of a Switched Linear System
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Hybrid systems are dynamic systems that arise out of the interaction of continuous state dynamics and discrete state dynamics. Switched systems, which are a type of hybrid system, have been given much attention by control systems research over the past decade. Problems with the controllability, observability, converseability and stabilizability of switched systems have always been discussed. In this paper, the trend in research regarding the stability of switched systems will be investigated. Then the variety of methods that have been discovered by researchers for stabilizing switched linear systems with arbitrary switching will be discussed in detail.
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EXPONENTIAL STABILITY OF UNCERTAIN SWITCHED LINEAR SYSTEMS
– In this paper, sufficient conditions are proposed to investigate the robust stability of arbitrary switched linear systems with uncertain parameters belongs to the known intervals. In addition, a method is then established to determine the maximum intervals of parameters' variations which guarantee robust exponential stability of uncertain switched linear systems under arbitrary switching. In the proposed method, the known information about the parametric structure of uncertainties is considered; therefore it will result in less conservative stability margins. A generalization of the method is also provided to determine stability bounds on perturbations of entries in subsystem matrices, when subsystems are subjected to independent perturbations. Numerical examples are included to illustrate the effectiveness of the results, and compare them with the previous results. It is shown that the proposed methods provide stability intervals on the uncertain parameter for all switched linear systems which admit a common quadratic Lyapunov function for the nominal system.
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A general stability criterion for switched linear systems having stable and unstable subsystems
International Journal of Adaptive Control and Signal Processing, 2012
SUMMARYWe report conditions on a switching signal that guarantee that solutions of a switched linear system converge asymptotically to zero. These conditions apply to continuous, discrete‐time and hybrid switched linear systems, those having both stable subsystems and mixtures of stable and unstable subsystems. Copyright © 2012 John Wiley & Sons, Ltd.
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Analysis of switched and hybrid systems-beyond piecewise quadratic methods
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Abstract This paper presents a method for stability analysis of switched and hybrid systems using polynomial and piecewise polynomial Lyapunov functions. Computation of such functions can be performed using convex optimization, based on the sum of squares decomposition of multivariate polynomials.
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