A Dynamic Event-Triggered Approach to H ∞ Control for Discrete-Time Singularly Perturbed Systems With Time-Delays and Sensor Saturations

TLDR: A novel Lyapunov–Krasovskii functional dependent on the singular perturbation parameter (SPP) is constructed, and an output-feedback controller design scheme is developed to ensure that, for any SPP not exceeding a prescribed upper bound, the closed-loop system is asymptotically stable with a guaranteed performance index.

Abstract: In this article, the $H_{\infty }$ control problem is investigated for a class of discrete-time singularly perturbed systems (DTSPSs) with time-delays and sensor saturations. In order to save the network bandwidth with satisfactory communication reliability during the signal transmissions, a dynamic event-triggered mechanism (DETM) is put forward to regulate the data-packet transmissions from the saturated sensors to the proposed controller. By constructing a novel Lyapunov–Krasovskii functional dependent on the singular perturbation parameter (SPP), the dynamics of the DTSPSs under the DETM are rigorously analyzed, and an output-feedback controller design scheme is then developed to ensure that, for any SPP not exceeding a prescribed upper bound, the closed-loop system is asymptotically stable with a guaranteed $H_{\infty }$ performance index. By resorting to the convex programming techniques, the desired controller gain is parameterized in light of the feasible solutions to a set of matrix inequalities. Finally, the effectiveness and merits of the proposed algorithm are demonstrated by a simulation example.