Passivity Analysis and Passification of Markovian Jump Systems

Abstract

This paper is concerned with the problems of delay-dependent robust passivity analysis and robust passification for uncertain Markovian jump linear systems (MJLSs) with time-varying delay. The parameter uncertainties are time varying but norm bounded. For the robust passivity problem, the objective is to seek conditions such that the closed-loop system under the state-feedback controller with given gains is passive, irrespective of all admissible parameter uncertainties. For the robust passification problem, desired passification controllers will be designed which guarantee that the closed-loop MJLS is passive. By constructing a proper stochastic Lyapunov-Krasovskii function and employing the free-weighting matrix 710 Circuits Syst Signal Process (2010) 29: 709-725 technique, delay-dependent passivity/passification performance conditions are formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed approaches is demonstrated by a numerical example.

Passivity-based sliding mode control for uncertain Markovian jump systems with time-varying delays

“…Given scalar τ > 0 and μ, the sliding mode dynamic system in (12) is passive in the sense of Definition 1 for any time-varying delay τ (t) satisfying (3), if there exist matrices S > 0, Z > 0, P i > 0, Q i > 0, W 1i , W 2i , i ∈ S, and scalars γ ≥ 0 and ε > 0, such that the following LMIs (13), (14) hold for all i ∈ S: where…”

“…Passivity theory provides a nice tool for studying stability of uncertain or nonlinear systems, especially for high-order systems. Thus the passivity analysis approach has been used in control problems for a long time to deal with robust stability problems for complex uncertain systems [6,12,13]. However, to the best of our knowledge, the problem of SMC with passivity for uncertain Markovian jump systems with time-varying delays have not been fully investigated and still remain open and challenging, to reduce the conservativeness, which motivates us to carry out the present study.…”

Passivity-based Control for Markovian Jump Systems via Retarded Output Feedback

“…Differently from [22,31], we employ an augmented Lyapunov functional approach, rather than free-weighting matrix approach, to obtaining the delay-dependent passivity criterion. The criterion has the advantage that one can make a tradeoff between conservatism and computational cost according to different practical conditions.…”

“…Specifically, for Markovian jump systems, the passivity criterion was developed in [7,22]. The feedback passification problem was considered in [16,31], where some state feedback controllers were designed such that the closed-loop system is passive. It is worth mentioning that the design of state feedback controllers requires the condition that all state variables are available, which is not always possible in practical applications.…”

Passivity and passification of stochastic impulsive memristor‐based piecewise linear system with mixed delays

“…The delay in the memristor‐based system has been considered by researchers recently . And the problem of time delay has been extensively studied . Moreover, time delays occur and vary frequently in those engineering, biological, and economical systems and, sometimes, depend on the histories heavily and result in oscillation and instability of systems .…”