Abstract
The current study addresses the mixed incremental H∞ and incremental passivity analysis for Markov switched stochastic (MSS) nonlinear systems. The multiple Lyapunov functions approach and the structure of Markov framework are utilized to establish some sufficient conditions for the MSS nonlinear systems, which will be used for the incrementally globally asymptotically stable in the mean(IGASiM) and performance index analysis. Then, the mixed incremental H∞ and incremental passivity performance issues are solved for two instances: in the first case, all subsystems are not IGASiM, while in the second one, both of IGASiM and unstable subsystems exist. Hence, it is shown that when none of the subsystems is IGASiM, the MSS nonlinear systems are IGASiM and possess the mixed incremental H∞ and incremental passivity performance metric in the presence of specified conditions. The mathematical induction is selected to guarantee the robust incremental stability of MSS systems with IGASiM and non-IGASiM subsystems and the performance index can be exhibited a prescribed decay rate. The effectiveness of the proposed results is demonstrated by two simulation examples.
Highlights
Stochastic hybrid systems include a group of dynamic systems consisting of continuous-time systems combined with discrete-time parts influencing by the measurement noise and discrete random events
These systems can be described by a variety of models, including stochastic switched systems [1], Markov jump systems [2]–[4], impulsive stochastic systems [5], [6]
Based on the stationary distribution of Markovian switching procedure, some sufficient conditions represented by inequalities are established and the incremental H∞ and incremental passivity performance problem to be solvable can be ensured
Summary
Stochastic hybrid systems include a group of dynamic systems consisting of continuous-time systems combined with discrete-time parts influencing by the measurement noise and discrete random events. These systems can be described by a variety of models, including stochastic switched systems [1], Markov jump systems [2]–[4], impulsive stochastic systems [5], [6]. MSS systems include a category of different active subsystems under actions governing a continuous-time Markov system, which can take values in defined state space. The incremental Lyapunov function was employed to ensure that the switching law achieves the stabilization of the MSS nonlinear systems. A continuous function β : R+ × R+ → R+ belongs to class KL if β(·, r) ∈ K and β(r, ·) is decreasing to zero for any fixed r ≥ 0
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