Abstract
SummaryThis paper is concerned with the optimal time‐weighted H2 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 H2 norm of the corresponding error system is minimized for a given mean square stable discrete MJLSs. The notation of time‐weighted H2 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 H2 norm formula, we propose a gradient flow method to solve the optimal time‐weighted H2 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.
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