Robust reliable <i>L</i>₂ – <i>L_∞</i> control for continuous‐time systems with nonlinear actuator failures

Abstract

This article examines the reliable L 2 – L ∞ control design problem for a class of continuous‐time linear systems subject to external disturbances and mixed actuator failures via input delay approach. Also, due to the occurrence of nonlinear circumstances in the control input, a more generalized and practical actuator fault model containing both linear and nonlinear terms is constructed to the addressed control system. Our attention is focused on the design of the robust state feedback reliable sampled‐data controller that guarantees the robust asymptotic stability of the resulting closed‐loop system with an L 2 – L ∞ prescribed performance level γ &gt; 0, for all the possible actuator failure cases. For this purpose, by constructing an appropriate Lyapunov–Krasovskii functional (LKF) and utilizing few integral inequality techniques, some novel sufficient stabilization conditions in terms of linear matrix inequalities (LMIs) are established for the considered system. Moreover, the established stabilizability conditions pave the way for designing the robust reliable sampled‐data controller as the solution to a set of LMIs. Finally, as an example, a wheeled mobile robot trailer model is considered to illustrate the effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 309–319, 2016