Robust and reliable ${\cal H}_∞$ control using LMI and ARE approaches

Abstract

Both robust and reliable control problems are matters of great interest in view of real-world control systems. Since such systems can be damaged by averse effects such as model uncertainties, exogenous disturbances, occasional component failures and so on, its stabilizing controller often need to construct with guaranteed robustness and reliability. Thanks to $H_∞$ control theory since 80``s, many researchers on that field have addressed the robust and reliable control methodologies to cope with these problems. However, most controllers are designed to be static one for the purpose to stabilize the control system against various uncertainties and multiple component failures, or use conventional algebraic Riccati equation(ARE) approach which requires some nonlinear or coupled solutions. In this dissertation, new robust and reliable control methods based on fault accommodation and linear matrix inequality(LMI) approach are proposed to solve these difficulties. The main contents are organized as follows. First, new robust and reliable $H_∞$ control algorithms are suggested for discrete-time uncertain systems with time-varying norm-bounded parameter uncertainty in the state matrix as well as with actuator failure among a prespecified subset of actuators. State feedback controllers can be obtained by deriving and solving modified parameter-dependent Riccati equations, which can stabilize the plant and guarantee a given $H_∞$-norm bound on attenuation of augmented disturbances - all admissible uncertainties as well as actuator failure. According to whether the process of fault accommodation is used or not, two robust and reliable $H_∞$ controllers are derived respectively by fixed and reconfigurable schemes. Performances of two controllers are evaluated through simulation studies for various failures. Next, robust and reliable $H_∞$ state-feedback or output-feedback controllers based on LMI approach are designed for linear uncertain systems. It is assumed that the...