L(2)-L(Infinity) Pid Output-Feedback Control For Discrete Time-Delay Systems

This paper is concerned with the l(2)-l(infinity) proportional-integral-derivative (PID) control problem for an array of linear discrete-time systems subject to time-varying delays. The accumulative sum-loop term (the integral term corresponding to the continuous-time situation) in the proposed PID controller is set to be performed over a limited time window for the sake of mitigating the accumulation error and the computational burden. The objective of the addressed problem is to develop an output-feedback-based PID control scheme so as not only to achieve the stability of the closed loop system in an exponential way but also to ensure the prescribed disturbance attenuation level in the l(2)-l(infinity) sense. The orthogonal decomposition technique is employed to deal with the nonlinear coupling term in matrix inequalities, and thereby the synthesis problem of the proposed PID controller is transformed into a convex optimization problem which can be easily solved via standard method. Finally, the validity of the developed controller design approach is exhibited by means of a simulation example.