Non-fragile reliable robust $$H_\\infty $$ controller synthesis for linear uncertain systems with integral quadratic constraints

Abstract

This paper presents a new approach to constructing a state-feedback fault-tolerant controller based on a robust $$H_\\infty $$\n control method. A class of linear time-invariant systems under consideration contains structured uncertainties satisfying integral quadratic constraints. A stabilizing solution to a parameterized $$H_\\infty $$\n -type Riccati equation is involved in constructing the controller such that the resulting closed-loop system is absolutely stable with a specified level of disturbance attenuation. This approach yields a robust controller that is not only reliable in the presence of actuator faults, but also non-fragile against uncertainties within itself. Moreover, a differential evolution algorithm is applied to optimize performance of the closed-loop system. Numerical examples are also presented to demonstrate the efficacy of our reliable robust control approach. It is shown in the examples that the disturbance attenuation levels of the reliable robust $$H_\\infty $$\n controllers synthesized using our approach are lower than those of other reliable $$H_\\infty $$\n controllers.