H [infinity symbol] 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

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Summary

Summary

Table of Contents