Stability Of Markovian Jump Systems Research Articles

Almost Sure Stability and Stabilization of Markovian Jump Systems With Stochastic Switching

This article addresses the exponential almost sure (EAS) stability and stabilization problems of continuous-time Markovian jump systems with additional stochastic switches. Sufficient conditions for EAS stability are established by applying a method to its stochastic transfer matrix. Particularly, both sojourn time and distribution of such random switchings are considered in the design of a state-feedback controller. Compared with some existing references, the proposed controller could bear unmatched or asynchronous signals. Moreover, it can be seen that our results are more general but less conservative, when the information on sojourn time and distribution is used. Some of them include previous work as special cases. Two examples are used to demonstrate the effectiveness and superiority of the methods proposed in our study.

Stabilization of Markovian Jump Systems With Quantized Input and Generally Uncertain Transition Rates

This study addresses the stabilization condition for Markovian jump systems with quantized input and generally uncertain transition rates. To stabilize Markovian jump systems with nonlinear inputs using only partial knowledge regarding to the transition rates, the proposed controller is designed as two control parts: a linear control part for stabilizing the system and a nonlinear control part for eliminating undesirable effects from the quantized input. Moreover, an appropriate weighting method, using lower and upper bounds of the partial transition rate, is employed to derive a less conservative stability condition. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed controller.

Restricted Stabilization of Markovian Jump Systems Based on a Period and Random Switching Controller

This paper considers the stabilization of continuous-time Markovian jump systems (MJSs) via a restricted controller. It is actually a period and random switching controller. It also contains some existing controllers as special ones. Sufficient conditions for existence of such a controller are established by studying a discrete-time MJS, which are presented in terms of LMIs and depend on its period and probability. Moreover, an extension about a similar but aperiodic controller is considered. Finally, a numerical example is used to demonstrate the effectiveness and superiority of the proposed methods.

Stabilization of Markovian Jump Systems With Stochastically Unmatched Mode

This paper considers the stabilization problem of continuous-time Markovian jump systems (MJSs) by applying a new controller. Different from the traditional methods, a kind of controller experiencing stochastically unmatched modes is proposed. More importantly, its mismatching property is modeled by a stochastically conditional probability and quantized by a given transition probability density function (PDF). Based on the proposed model, more general but less conservative results are presented in terms of linear matrix inequalities (LMIs). Then, some extensions about the expectation of truncated PDF matrix uncertain, partially known and nonsingular respectively are further considered. Finally, a practical example is used to illustrate the effectiveness and superiority of the developed theoretical results.

A Fuzzy Control Approach to Stabilization of Markovian Jump Systems with General Unknown Transition Probabilities

This paper is devoted to the investigation of the stability and stabilization problems for a class of Markovian jump nonlinear systems with general unknown transition rates (GUTRs) via fuzzy control. The Takagi-Sugeno (T-S) fuzzy model is utilized to characterize the Markovian jump nonlinear systems with general unknown transition probabilities. Some sufficient criteria on stochastic stability are derived in terms of linear matrix inequalities, and a mode-dependent fuzzy controller is designed. The derived results extend the conclusions recently presented by Sheng and Gao (Stabilization for Markovian jump nonlinear systems with partly unknown transition probabilities via fuzzy control, Fuzzy Set Syst 161(21): 2780–2792, 2010). In fact, the system discussed in Sheng and Gao (Fuzzy Set Syst 161(21) 2780–2792, 2010) is a special case of ours, because their transition rates are completely known or completely unknown, while in our GUTR T-S fuzzy model, each transition rate can be completely unknown or only its estimate value is known. Finally, a numerical example is present to illustrate the effectiveness and applicability of the proposed method.

New Results on Stability and Stabilization of Markovian Jump Systems with Time Delay

This technical paper deals with the problem of stochastic stability and stabilization for a class of linear Markovian jumping systems with discrete time-varying delay. A novel delay-dependent stochastic stability criterion for Markovian delay systems is established based on new augmented Lyapunov-Krasovskii functional and delay fractioning techniques. Then a state feedback controller is designed to guarantee the stochastic stability of the resulting closed-loop system. Numerical examples are provided to illustrate the effectiveness of the proposed design approach in this paper.

Stabilization of Discrete-Time Markovian Jump Systems via Controllers with Partially Mode-Dependent Characterization

A kind of stabilizing controller in terms of being partially mode-dependent is developed for discrete-time Markovian jump systems (MJSs). The property referred to be partially mode-dependent is described by the Bernoulli variable. Based on the established model, the stabilization for MJSs over unreliable networks is considered, where both network-induced delay and packet dropout take place in system modes and states. Such effects of network are taken into account in controller design. All the conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the effectiveness and applicability of the proposed method.

State estimation for Markovian jump systems with time-varying delay and partial information on transition probabilities

This study investigates the state estimation problem for a class of continuous-time Markovian jump systems (MJSs) with time-varying delay and partial information on transition probabilities. The novel sufficient conditions are established to guarantee the mean square stability of MJSs via introducing the free-connection weighting matrices. As a result, the state estimators are designed to estimate original systems through available output measurement. Finally, numerical examples and simulations are given to illustrate the effectiveness and the merits of the proposed method.

Stability and Stabilization of Markovian Jump Systems With Time Delay Via New Lyapunov Functionals

This paper is concerned with the mean square exponential stability and stabilization problems of Markovian jump systems with time delay. New Lyapunov functionals are proposed by choosing distinct Lyapunov matrices for different system modes and introducing a triple-integral term. Some delay-dependent conditions, including some existing results as their special cases, are derived under which the resulting closed-loop system is mean square exponentially stable with a decay rate. The design of the feedback gain matrices is accomplished by solving linear matrix inequalities. Finally, the effectiveness and performance of the obtained results are demonstrated by numerical examples.

Mode-Independent Stabilization of Markovian Jump Systems With Time-Varying Delays: A Sliding Mode Approach

This paper investigates mode-independent stabilization of Markovian jump systems with time-varying delays via a sliding mode approach. A sufficient condition is proposed to guarantee the existence of a mode-independent sliding surface. Because the real plant regime mode is not directly accessible and instantly available, a controller is reconfigured online by calculating a detection function such that the closed-loop system converges to the sliding surface in finite time. A comparison example is presented to illustrate merits of the developed theory.

New Results on Stability and Stabilization of Markovian Jump Systems with Partly Known Transition Probabilities

This paper investigates the problem of stability and stabilization of Markovian jump linear systems with partial information on transition probability. A new stability criterion is obtained for these systems. Comparing with the existing results, the advantage of this paper is that the proposed criterion has fewer variables, however, does not increase any conservatism, which has been proved theoretically. Furthermore, a sufficient condition for the state feedback controller design is derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Stochastic Stabilization of Markovian Jump Systems with Partial Unknown Transition Probabilities and Actuator Saturation

The stochastic stabilization problem of Markovian jump systems subject to both partial unknown transition probabilities and actuator saturation is considered in this paper. Different from the previous results where complete knowledge on the transition probabilities is available, a new controller synthesis scheme is proposed as well as an estimate of the domain of attraction in mean square sense. A sufficient condition is first established to guarantee the stochastic stability of the closed-loop system. An optimization problem with LMI constraints is then formulated to determine the largest contractively invariant set in mean square sense. Finally, a numerical example is provided to show the effectiveness of our method.