(A) study on robust and reliable $H_∞$ control for uncertain linear systems

Abstract

Uncertainties and component failures are frequently encountered in real-world control systems. Inherent in real-world systems is the fact of uncertainty. And each component of a control system is subjected random failures due to both internal causes and external causes. This thesis focuses on the problem of robust and reliable $H_{\infty}$ control design for linear systems under uncertainties and component failures. The uncertainties considered here are a time-varying norm-bounded parameter uncertainty in the state matrix, disturbance inputs in the state equation and measurement noises. Actuator and/or sensor failures are studied as component failures whose outputs are assumed to be any arbitrary energy-bounded signals. In the designs, failure signals are treated as disturbance inputs to the system. First a state feedback control design is presented that stabilizes the plant and guarantees and $H_{\infty}$-norm bound constraint on attenuation of augmented disturbances, including failure signals, for all admissible uncertainties as well as actuator failures. A construction of the desired state feedback control law is given in terms of a positive-definite solution of a parameter-dependent algebraic Riccati equation. Necessary conditions for the existence of controller are derived. And an observer-based output feedback controller design is presented which stabilizes the plant and guarantees an $H_{\infty}$-norm bound on attenuation of augmented disturbances, including failure signals, for all admissible uncertainties as well as actuator and/or sensor failures. A construction of the observer-based output feedback control law requires the positive-definite solutions of two algebraic Riccati equations. The results of this thesis provides a solution for robust control and reliable control at the same time, and also extends previous results on robust $H_{\infty}$ control and reliable $H_{\infty}$ control of uncertain linear systems to robust and reliable $H_{infty}$ co...