Stabilization by Quantized Delayed State Feedback
Résumé
This chapter is devoted to the design of a static-state feedback controller for a linear system subject to saturated quantization and delay in the input. Due to quantization and saturation, we consider, for the closed-loop system, a weaker notion of stability, namely local ultimate boundedness. The closed-loop system is then modeled as a stable linear system subject to discontinuous perturbations. Then by coupling a certain Lyapunov–Krasovskii functional via S-procedure to adequate sector conditions, we derive sufficient conditions to ensure for the trajectories of the closed-loop system finite time convergence into a compact Su surrounding the origin, from every initial condition belonging to a compact set S0. Moreover, the size of the initial condition set S0 and the ultimate set Su are then optimized by solving a convex optimization problem over linear matrix inequality (LMI) constraints. Finally, an example extracted from the literature shows the effectiveness of the proposed methodology.