H-infinity Control and Estimation of State-multiplicative Linear Systems

Control and estimation of linear systems with state-multiplicative noise in the H-infinity setting is covered in this monograph. Multiplicative noise appears in systems where the process or measurement noise levels depend on the system state vector. Such systems are relevant when a gain-scheduled controller utilizes a noisy gain-scheduling parameter or when the noise level depends on one or more of the states; the latter is encountered, for example, in radar measurements where larger ranges involve higher noise level. The last decade has witnessed a resurgence of interest in the study of these systems, which constitute a special class of nonlinear systems, mainly in the field of H-infinity control.

H-infinity Control and Estimation of State-multiplicative Linear Systems embodies a comprehensive survey of the relevant literature with basic problems being formulated and solved by applying various techniques including game theory, linear matrix inequalities and Lyapunov parameter-dependent functions.

Topics covered include:

• practical problems in which state-multiplicative noise has to be dealt with;
• convex H₂ and H-infinity norms analysis of systems with multiplicative noise;
• state feedback control and state estimation of systems with multiplicative noise;
• dynamic and static output feedback of stochastic bilinear systems;
• tracking controllers for stochastic bilinear systems utilizing preview information.

Various examples which demonstrate the applicability of the theory to practical control engineering problems are considered; two such examples are taken from the aerospace and guidance control areas.