Model reduction of discrete Markovian jump systems with time‐weighted H 2 performance

作者：Minhui Sun, James Lam · 发表于：International Journal of Robust and Nonlinear Control · 年份：2015 · DOI：10.1002/rnc.3315 · 被引用次数：9 · 研究领域：Stability and Control of Uncertain Systems、Control Systems and Identification、Fault Detection and Control Systems

Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.