Robust Stabilization of Discrete time Constrained Singular Piecewise affine Systems with Norm bounded Uncertainties

Jinhai Sun, Jinhai Li, Haiyang Liu, Feng Wang , Yuepeng Yan

(Institute of microelectronics, Chinese Academy of Sciences, Beijing 100029, China)



Abstract:

In this paper, the problem of designing robust H ª«infinityª« output feedback controller and lª­2 ª«gainª« controller are investigated 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 ª«infinityª« stabilization condition is established and the lª­2 ª«gainª« controller is investigated, and meanwhile, the input saturation disturbance tolerance condition is proposed. Under energy bounded disturbance, the domain of attraction is well estimated and the lª­2 ª«gainª« controller is designed in some restricted region. It is shown that the controller gains 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 ª«infinityª« performance ¦Ã is minimized. Finally, numerical examples are given to illustrate the effectiveness of the proposed design methods.

Key words:  singular piecewise affine systems  input and state constraints  output feedback control  LMIs  singular piecewise Lyapunov function

DOI£º10.11916/j.issn.1005-9113.2015.01.007

Clc Number:TP273

Fund: