Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

Abstract

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function

Probability-Guaranteed $H$_∞-Filtering for 2$D$-Systems with Random Nonlinearities and Missing Measurements

“…Two-dimensional systems with information propagation in two independent directions have attracted considerable attention due to applications in image data processing and transmission, biomedical imaging processing, multidimensional digital filtering, thermal processes, and water stream heating [2,6,10]. In particular, for 2D-systems asymptotic and exponential stability are studied in [24], controller design problems in [4,16], stability analysis and stabilisation of switched systems in [1,21], and H ∞ -control problems for Markovian jump systems with state-delays and defective mode information in [20]. There are also results concerning the H ∞ -filtering design approach -e.g.…”

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

“…In the recent past, the guaranteed cost control problem for 2-D discrete uncertain systems has attracted several researchers (Dhawan and Kar, 2007a, 2007b, 2007c, 2010, 2011a, 2011b; Guan et al, 2001; Tiwari and Dhawan, 2012a). The aim of guaranteed cost control is to design a controller such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties.…”