Robust Stability Analysis of Linear Parameter-Varying Systems With Markov Jumps
Alessandro N. Vargas, Cristiano Marcos Agulhari, Ricardo C. L. F. Oliveira, Víctor M. Preciado
Abstract
This article presents conditions to assure the mean-square stability of linear parameter-varying systems with Markov jumps. The model dynamics are driven not only by a Markov chain but also by time-varying parameters that take values in a polytopic set. No assumption is imposed on how the parameters vary within the polytopic set, i.e., the variation rate can be arbitrarily fast. The proposed conditions stem from a homogeneous polynomial Lyapunov function in the state space, adapted to account for Markov jumps. The stability certificate is sought through linear matrix inequalities. Numerical examples illustrate this article’s contribution.
Topics & Concepts
Control theory (sociology)Stability (learning theory)Linear systemMarkov chainMarkov processMathematicsComputer scienceApplied mathematicsStatisticsArtificial intelligenceControl (management)Mathematical analysisMachine learningStability and Control of Uncertain SystemsControl Systems and IdentificationAdvanced Control Systems Optimization