Model reduction of discrete Markovian jump systems with time‐weighted H₂ performance

Abstract

This paper is concerned with the optimal time-weighted H 2 model reduction problem for discrete Markovian jump linear systems (MJLSs). The purpose is to find a mean square stable MJLS of lower order such that the time-weighted H 2 norm of the corresponding error system is minimized for a given mean square stable discrete MJLSs. The notation of time-weighted H 2 norm of discrete MJLS is defined for the first time, and then a computational formula of this norm is given, which requires the solution of two sets of recursive discrete Markovian jump Lyapunov-type linear matrix equations. Based on the time-weighted H 2 norm formula, we propose a gradient flow method to solve the optimal time-weighted H 2 model reduction problem. A necessary condition for minimality is derived, which generalizes the standard result for systems when Markov jumps and the time-weighting term do not appear. Finally, numerical examples are used to illustrate the effectiveness of the proposed approach.M. SUN AND J. LAM where x.k/ 2 R n represents the state variable of the system, u.k/ 2 R p is the control input vector, and´.k/ 2 R m is the output. The parameter Â.k/ stands for the state of a Markov

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