Uncertain Two-dimensional Discrete Systems Research Articles

Robust $$H_{\infty }$$ filtering for uncertain two-dimensional discrete systems with state-varying delays

Robust $$H_{\infty }$$ filtering for uncertain two-dimensional discrete systems with state-varying delays

Parameter-dependent robust H∞ filtering for uncertain two-dimensional discrete systems in the FM second model

Abstract This paper deals with the problem of robust $H_{\infty }$ filtering for uncertain two-dimensional discrete systems in the Fornasini–Marchesini second model with polytopic parameter uncertainties. Firstly, a new $H_{\infty }$ performance criterion is derived by exploiting a new structure of the parameter-dependent Lyapunov function. Secondly, based on the criterion obtained, a new condition for the existence of a robust $H_{\infty }$ filter that ensures asymptotic stability, and a prescribed $H_{\infty }$ performance level of the filtering error system, for all admissible uncertainties is established in terms of linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness and advantage of the proposed method.

New Relaxed Stability Conditions for Uncertain Two-Dimensional Discrete Systems

This paper is concerned with the problem of robust stability of uncertain two-dimensional (2-D) discrete systems described by the Roesser model with polytopic uncertain parameters. Based on a newly developed parameter-dependent Lyapunov–Krasovski functional combined with Finsler’s lemma, new sufficient conditions for robust stability analysis are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservatism of the proposed results.

Delay-dependent robust stability and stabilisation of uncertain two-dimensional discrete systems with time-varying delays

The problems of delay-dependent robust stability and stabilisation for a class of uncertain two-dimensional (2-D) discrete systems with time-varying delays described by the second Fornasini-Marchesini local state space (FM LSS) model are investigated in this study. By employing improved free-weighting matrix approach, delay-dependent stability criterion for the nominal 2-D state-delayed system is first obtained and formulated in terms of linear matrix inequalities (LMIs); and then, a stabilisation design criterion using static state feedback controller is derived based on the stability result. Since the design criterion is not expressed strictly in terms of LMI, an improved cone complementary linearisation algorithm is employed to solve the non-convex feasibility problem. Furthermore, the stability and stabilisation results are extended to robust stability and stabilisation of the uncertain 2-D state-delayed system. Numerical examples are provided to demonstrate the effectiveness and advantage of the proposed method.

Robust H ∞ filtering for uncertain two-dimensional discrete systems with state-varying delays

This paper is concerned with the problem of robust filtering for uncertain 2-D discrete sys- tems in Fornasini-Marchesini second local state-space model with state-varying delays. The parameter uncertainty is assumed to be norm-bounded. A 2-D stable filter is designed to ensure that a prescribed H∞ performance level is fulfilled for all admissible uncertainties. A linear matrix inequality (LMI) ap- proach is developed to solve the above problem, and delay-dependent conditions for the solvability are obtained. A illustrative example is provided to demonstrate the feasibility and effectiveness of the pro- posed method.

ℋ∞ model reduction for uncertain two-dimensional discrete systems

This paper investigates the problem of ℋ∞ model reduction for two-dimensional (2-D) discrete systems with parameter uncertainties residing in a polytope. For a given robustly stable system, our attention is focused on the construction of a reduced-order model, which also resides in a polytope and approximates the original system well in an ℋ∞ norm sense. Both Fornasini–Marchesini local state-space (FMLSS) and Roesser models are considered through parameter-dependent approaches, with sufficient conditions obtained for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be readily solved using standard numerical software. In addition, the development of zeroth order models is also presented. Two numerical examples are provided to show the effectiveness of the proposed theories. Copyright © 2005 John Wiley & Sons, Ltd.

Stability analysis and stabilization of uncertain two-dimensional discrete systems: an LMI approach

The authors consider the problem of robust stability analysis and stabilization of uncertain two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (LSS) model. Sufficient conditions for the uncertain 2-D discrete systems to be robustly stable are given in terms of linear matrix inequalities (LMI's). The LMI approach is also introduced to solve the robust stabilization problem of the uncertain 2-D systems via static-state feedback. Furthermore, sufficient conditions for the 2-D uncertain systems to be free of overflow oscillations under a saturation arithmetic are established.