Guaranteed cost PID control for uncertain discrete‐time stochastic systems with additive gain perturbations

This paper investigates a novel design method for robust nonfragile proportional‐integral‐derivative (PID) control that is based on the guaranteed cost control (GCC) problem for a class of uncertain discrete‐time stochastic systems with additive gain perturbations. On the basis of linear matrix inequality (LMI), a class of fixed PID controller parameters is obtained, and some sufficient conditions for the existence of the GCC are derived. Although the additive gain perturbations are included in the feedback systems, both the stability of closed‐loop systems and adequate cost bound are attained. As a sequel, decentralized GCC PID for a class of discrete‐time uncertain large‐scale stochastic systems is also considered. Finally, the numerical results demonstrate the efficiency of the proposed controller synthesis. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society