Model reduction for discrete-time periodic systems with dissipativity

This paper is concerned with the model reduction problem for discrete-time periodic systems with time-varying delay. By utilising an adjusted reciprocally convex combination approach, some sufficient criteria are established to guarantee that the discrete-time periodic system with time-varying delay is asymptotically stable. Then, the reduced-order model is designed to approximate the original system. In the design, both the dissipativity and the Hankel norm performances are considered to test the model approximation, and correspondingly, the conditions are also established, which guarantee that the approximation error system is asymptotically stable with the dissipativity performance and the Hankel norm property, respectively. The convex linearisation and the projection are presented to design the reduced-order model, respectively. Finally, numerical examples are provided to verify the effectiveness of the design scheme.