ℓ2-ℓ∞ PID Output-Feedback Control for Discrete Time-Delay Systems*

This paper is concerned with the ℓ2-ℓ∞ 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 ℓ2-ℓ∞ 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.

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