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

Multiplicative noise appears in systems where the process or measurement noise levels depend on the system state vector. Such systems are relevant, for example, in radar measurements where larger ranges involve higher noise level.

This monograph 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: 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.

Part I: Introduction and Literature Survey: Introduction.- Part II: Continuous-time Systems: Control and Luenberger-type Filtering; General Filtering; Tracking Control; Static Output-feedback; Stochastic Passivity.- Part III: Discrete-time Systems: Control and Luenberger-type Filtering; General Filtering; Tracking Control; Static Output-feedback.- Part IV: Applications: Systems with State-multiplicative Noise: Applications.- Appendix A Introduction to Stochastic Differential Equations.- Appendix B The Continuous DLMI Method.- Appendix C The Discrete DLMI Method.