H ∞ Model Reduction of 2D Markovian Jump System with Roesser Model

Abstract: This paper extends the results obtained for one-dimensional Markovian jump systems to investigate the problem of H ∞ model reduction for a class of linear discrete time 2D Markovian jump systems with state delays in Roesser model which is time-varying and mode-independent. The reduced-order model with the same randomly jumping parameters is proposed which can make the error systems stochastically stable with a prescribed H ∞ performance. A sufficient condition in terms of linear matrix inequalities (LMIs) plus matrix inverse constraints are derived for the existence of a solution to the reduced-order model problems. The cone complimentarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints. A numerical example is given to illustrate the design procedures