Robustness Of Markov System And Its Applications In Multi-agent Systems

Markov jump linear systems (MJLSs) are a class of linear systems with Markovjumping parameters. Their model includes two components: the mode described byMarkov process and the state in every mode represented by di?erential equations. Com-pared with traditional control systems, MJLSs can better re?ect all kinds of randommutation factors of the practical control problem, such as sudden environment changes,changes in the interconnections of subsystems and so on. In the past decade, MJLSshave received much attention, due to their profound practical application background.For uncertain discrete-time MJLSs, this paper studies the robust stochastic stabiliza-tion, H∞control problem and their applications in multi-agent systems. The mainconclusions and contribution of this paper are as follows:First, for MJLSs with norm bounded uncertainties, we just consider the robuststochastic stabilization via two di?erent state feedback control laws. By the vari-able substitution, the original MJLSs are transformed into an equivalent new MJLSs.Through generalizing the system's dimension and using the stochastic Lyapunov func-tion method, su?cient conditions for testing the robust stochastic stabilization and H∞performance index of MJLSs are established in terms of linear matrix inequalities, re-spectively. Second, this paper studies the consentability of multi-agent systems withstochastic switching topology. And some criteria for testing the consentability of suchsystems are established.