Filtering for uncertain 2-D discrete systems with state delays

• Published in: Signal processing Vol. 87; no. 9; pp. 2213 - 2230
• Main Authors: Wu, Ligang, Wang, Zidong, Gao, Huijun, Wang, Changhong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2007; Elsevier Science
• Subjects: [formula omitted] norm; Applied sciences; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Filtering; Information, signal and communications theory; Linear matrix inequality (LMI); Signal and communications theory; Signal, noise; Telecommunications and information theory; Time-delay; Two-dimensional (2-D) systems; Time-delay; Filtering; Two-dimensional (2-D) systems; Linear matrix inequality (LMI); H ∞ norm; Performance evaluation; H infinite optimization; Non linear filter; H infinite control; Two dimensional model; Discrete system; State space method; H∞ norm; Convex programming; Robust control; Asymptotic stability; Sufficient condition; Simulation; Discrete time; Linear matrix inequality; Delay time
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2007.03.002

This paper is concerned with the problem of robust H ∞ filtering for two-dimensional (2-D) discrete systems with time-delays in states. The 2-D systems under consideration are described in terms of the well-known Fornasini–Marchesini local state-space (FMLSS) models with time-delays. Our attention is focused on the design of a full-order filter such that the filtering error system is guaranteed to be asymptotically stable with a prescribed H ∞ disturbance attenuation performance. Sufficient conditions for the existence of desired filters are established by using a linear matrix inequality (LMI) approach, and the corresponding filter design problem is then cast into a convex optimization problem that can be efficiently solved by resorting to some standard numerical software. Furthermore, the obtained results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. A simulation example is provided to illustrate the effectiveness of the proposed design method.