Robust Filter Design Based On Polynomially Parameter-dependent Lyapunov Functions

The filtering problem is one of producing an estimate of the system state usingmeasurements, while robust filtering is to estimate an unknown hidden state whenthe system model exists uncertainty. This dissertation is concerned with the problemof robust filter design for a class of convex polyhedron uncertain systems, includ-ing linear systems, time-delay systems, multi-dimensional systems, and conservatismreduction issues are discussed.Robust filter design methods for uncertain continuous and discrete-time systemshave been proposed in Chapter 2. Based on this, Chapter 3 studies the problem of de-signing robust H∞filters for uncertain time-varying delay systems in both continuous-and discrete-time cases. Moreover, Chapter 4 considers the robust H∞filtering prob-lem for 2D discrete systems which have strong application backgrounds in signalprocessing and heat energy engineering etc. Linear matrix inequality (LMI) condi-tions are obtained for the existence of admissible filters and based on polynomiallyparameter-dependent matrices of arbitrary degree, the filter design problems are castinto convex optimizations, which can be readily solved via standard numerical soft-ware. Due to its utilization of a common Lyapunov function for the entire uncertaintydomain, quadratic stability has been well recognized to be conservative, which pre-vents robust control theory from further development and limits its applications.This thesis, based on previous works of others, systematically and deeply investi-gates the problems of filter design for polytopic uncertain systems in both continuous-and discrete-time cases based on polynomially parameter-dependent Lyapunov func-tions, and presents analysis and synthesis methodologies for uncertain dynamic sys-tems in the unified polynomially parameter-dependent framework. In aerospace, as-tronautics and industrial process, it is usually difficult to characterize the dynamics ofthe controlled object exactly by a mathematical model, therefore the problem investi-gated in this paper is of great theoretical and practical significance.