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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 878120, 16 pages
Research Article

Robust H-Infinity Stabilization and Resilient Filtering for Discrete-Time Constrained Singular Piecewise-Affine Systems

Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150080, China

Received 7 June 2014; Accepted 12 November 2014

Academic Editor: Asier Ibeas

Copyright © 2015 Zhenhua Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the problem of designing robust H-infinity output feedback controller and resilient filtering for a class of discrete-time singular piecewise-affine systems with input saturation and state constraints. Based on a singular piecewise Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, the H-infinity stabilization condition is established and the resilient H-infinity filtering error dynamic system is investigated, and, meanwhile, the domain of attraction is well estimated. Under energy bounded disturbance, the input saturation disturbance tolerance condition is proposed; then, the resilient H-infinity filter is designed in some restricted region. It is shown that the controller gains and filter design parameters can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Meanwhile, by using the corresponding optimization methods, the domain of attraction and the disturbance tolerance level is maximized, and the H-infinity performance is minimized. Numerical examples are given to illustrate the effectiveness of the proposed design methods.