Stability analysis of linear control systems with uncertain parameters

In this dissertation, we study stochastic stability of linear systems whose parameters are randomly varying in a certain sense. In particular, we present a new approach to stochastic stability analysis of systems whose system structure is randomly changing among a finite set of possibilities which capture the abrupt changes in systems parameters or sudden failures of system components. These types of systems are referred to as jump linear systems with a finite state Markov chain form process.;We first investigate the properties of various types of moment stability for stochastic jump linear systems, and use large deviation theory to study the relationship between "lower moment" stability and almost sure stability. In particular, we have proved that the region for ;This dissertation is the first research work in the current literature to use large deviation theory to study stochastic stability and further represents a systematic study of almost sure stability of jump linear systems with a finite state Markov chain form process. It is our high hope that this work will pave the way for further studies on the almost sure (sample path) stability for stochastic systems.