6 Stochastic Passivity

Abstract

Passivity of deterministic linear systems plays an important role in network theory and in adaptive control. The fact that a system is passive entails some stability properties that allow for robust control design of this system. It is the purpose of the present chapter to investigate the corresponding situation in linear systems with multiplicative noise. The concept of stochastic passivity is first considered and a positive-real like lemma for finite dimensional linear time invariant uncertain systems with state multiplicative noise is derived. The system uncertainties are assumed to be of the polytopic type.