Extremal storage functions and minimal realizations of discrete-time\n linear switching systems

2016/09/19 by Matthew Philippe, Philippe, Matthew, Ray Essick +5
Engineering · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1609.05779

openalex publication_date 2016/09/19 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study the \L_p induced gain of discrete-time linear switching\nsystems with graph-constrained switching sequences. We first prove that, for\nstable systems in a minimal realization, for every p \≥ 1, the\n\L_p-gain is exactly characterized through switching storage\nfunctions. These functions are shown to be the pth power of a norm. In order\nto consider general systems, we provide an algorithm for computing minimal\nrealizations. These realizations are \rectangular systems, with a state\ndimension that varies according to the mode of the system. We apply our tools\nto the study on the of \L₂-gain. We provide algorithms for its\napproximation, and provide a converse result for the existence of quadratic\nswitching storage functions. We finally illustrate the results with a\nphysically motivated example.\n

Citations

• Uniform stabilization of discrete-time switched and Markovian jump linear systems
• Feedback stabilization of dynamical systems with switched delays

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