$$H_{\infty }$$ Model Reduction for 2-D Discrete Markovian Jump Systems

Abstract

This paper is concerned with the problem of H ∞ model reduction for two-dimensional (2-D) discrete Markovian jump systems. The mathematical model of 2-D Markovian jump systems is described by the Fornasini-Marchesini (F-M) second model. Our attention is focused on the design of a 2-D reduced-order model, which ensures the model error system to be stochastically stable and has a prescribed H ∞ performance index. By using the Lyapunov functional approach and introducing some zero equations, a new condition for H ∞ performance analysis of model error system is developed. Based on this condition, the desired reduced-order model parameters can be obtained by solving a set of linear matrix inequalities. Two examples are presented to show the effectiveness of the proposed method. Keywords 2-D systems • Markovian jump • Model reduction • H ∞ performance • Linear matrix inequalities B Khalid Badie

Output tracking control for 2‐D discrete systems with actuator failures

“…The filtering problem has been addressed in References 11‐14. The model approximation problem has been considered in References 15‐18. In addition, the Roesser model is widely used due to its simplicity and generality.…”

Robust ∞ model reduction for the continuous fractional‐order two‐dimensional Roesser system: The 0 < ε ≤ 1 case

“…The subject of $$$ {H}_{\infty } $$$ model reduction for discrete integer‐order 2D singular Roesser system has been studied in [13], and the parameters of the reduced‐order system can be calculated by solving linear matrix inequalities (LMIs). The problem of $$$ {H}_{\infty } $$$ model reduction for discrete integer‐order 2D Markovian jump systems has been investigated in [14]. With the help of the Finsler's lemma, the problem of $$$ {H}_{\infty } $$$ model reduction for continuous integer‐order 2D systems with finite frequency ranges has been discussed in [15].…”