Distributed control for spatially interconnected time-varying delay systems under input saturation

This paper presents the distributed control design for a class of spatially interconnected continuous-time time-varying delay (SICTD) systems under input saturation. A distributed controller and distributed anti-windup compensator (AWC) are proposed based on the distributed structure of the SICTD system. Then, a sufficient condition is derived to guarantee the asymptotic stability and $H_{\infty }$ performance of the closed-loop system under the saturation constraints. We have also provided an algorithm for obtaining the AWC parameters by employing the elimination lemma and the cone complementary linearization approach. The proposed anti-windup compensation methodology can also be employed to compensate for the actuator saturation of the spatially interconnected delay-free systems. Finally, two practical examples are presented to verify the effectiveness of the proposed AWC design method.