Observer‐based non‐fragile control against measurement disturbances and controller perturbations for discrete systems with state delay

This paper investigates the observer-based non-fragile control problem for a class of discrete time delay systems with measurement disturbances and controller perturbations. A simultaneous state and disturbance estimation technique is developed by designing a state observer for a descriptor system obtained from the original system. Based on this observer, the design method of a non-fragile controller is then formulated and the controller design problem is transformed to a convex optimization problem, which can be solved by a linear matrix inequality approach. In this design, the additive and multiplicative forms of uncertainties which perturb the gains of control and observer are both considered. The resultant non-fragile observer-based controller guarantees that the closed-loop system is asymptotically stable and can tolerate measurement disturbances and a certain degree of controller parameter perturbation. A numerical example is given to illustrate the effectiveness of the proposed design method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society