Abstract
This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.
Highlights
In recent years, the research on two-dimensional (2-D) discrete systems have received considerable attention, since 2-D systems exist in many practical applications such as image data processing, seismographic data processing, thermal processes, gas absorption, water stream heating, river pollution modeling, etc. [1,2,3,4,5]
This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations
A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method
Summary
The research on two-dimensional (2-D) discrete systems have received considerable attention, since 2-D systems exist in many practical applications such as image data processing, seismographic data processing, thermal processes, gas absorption, water stream heating, river pollution modeling, etc. [1,2,3,4,5]. The aim of robust non-fragile control is to design a robust controller for a given uncertain system such that the controller is insensitive to some amount of error with regard to its gain Based on this idea, many significant results have been obtained for one-dimensional case [16,17,18,19,20,21,22]. This paper, deals with the problem of robust non-fragile control for a class of 2-D discrete uncertain systems described by the FMSLSS model.
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