Reliable dissipative sampled-data control for uncertain systems with actuator failures and application to vehicle dynamics

Abstract

This paper focuses on the dissipative reliable sampled-data control for a class of linear uncertain systems against actuator failures. The main purpose is to design a state feedback reliable dissipative control law such that the resulting closed-loop uncertain system is strictly $({\mathcal Q}, {\mathcal R}, {\mathcal S})-\theta $ dissipative for all admissible actuator failures with a certain prescribed performance constraint. By constructing a proper Lyapunov–Krasovskii functional based on sampled-data strategy, a set of sufficient condition for the existence of the controller is derived in terms of the linear matrix inequality (LMI) technique. It has also been shown that the solutions to the dissipative reliable sampled-data control can be obtained by solving the proposed LMIs. The main advantage of this paper is it unifies $H_\infty $ and passivity control and provides a more flexible control design as it allows for a better trade-off between phase and gain performances. Finally, a numerical example based on vehicle dynamics model is provided to demonstrate the effectiveness of the proposed design technique.