Title :
A bounded real lemma for jump systems
Author :
Seiler, Pete ; Sengupta, Raja
Author_Institution :
Dept. of Mech. & Ind. Eng., Univ. of Illinois, Urbana, IL, USA
Abstract :
This note presents a bounded real lemma for discrete-time Markovian jump linear systems (MJLSs). We show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems. For the case of one plant mode, this condition reduces to the standard necessary and sufficient condition for discrete-time systems. We envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for MJLSs.
Keywords :
discrete time systems; linear matrix inequalities; linear systems; stochastic systems; Markovian jump systems; bounded real lemma; discrete-time systems; linear matrix inequality; linear systems; necessary condition; stochastic Lyapunov function; sufficient condition; Control systems; Controllability; Linear matrix inequalities; Linear systems; Observability; Riccati equations; Stability; Stochastic processes; Stochastic systems; Sufficient conditions;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2003.817010
