Decentralized guaranteed cost PID control for uncertain large-scale deterministic and stochastic discrete-time systems with additive gain

This paper investigates a novel design method for robust proportional-integral-derivative (PID) control that is based on the decentralized guaranteed cost control (DGCC) problem for a class of discrete-time large-scale uncertain deterministic and stochastic systems with additive gain. 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 DGCC are derived. A novel concept is that the fixed PID controller parameters are combined with additive gain such as that in fuzzy control to enhance the transient stability. Although the additive gain is included in the feedback systems, the stability of closed-loop systems and desired transient response are both attained.