Generally Uncertain Transition Rates Research Articles

Stabilisation of Markov jump systems with input quantisation and general uncertain transition rates

This study addresses the problem of designing state feedback controllers for Markov jump systems subject to input quantisation mismatch, and general transition rates allowed to be uncertain and unknown. First, a non-linear control law is constructed for eliminating the effect of input quantisation in the presence of mismatch between quantisation parameters. Then, a new method based on vertex separator algorithm is proposed for designing the controller. A sufficient condition is derived such that the stochastic stability and also the disturbance attenuation performance of the resulting closed-loop system can be ensured. Moreover, it is proved that the obtained result is theoretically less conservative than previous results. Finally, numerical examples are presented to show the effectiveness and advantages of the proposed method.

Fault estimation for a class of nonlinear Markov jump systems with general uncertain transition rates

ABSTRACTThis paper addresses the problem of fault estimation for a class of nonlinear Markov jump systems with Lipschitz-type nonlinearities and general transition rates allowed to be uncertain and unknown. First, by introducing a mode-dependent intermediate variable, an intermediate estimator is proposed to estimate faults and state simultaneously. Then, a vertex separator is exploited to develop a sufficient condition for the fault estimator design in terms of linear matrix inequalities. The design guarantees the boundedness in probability of the estimation errors if the derivations of the faults are bounded. Further, it is proved that the proposed approach is less conservative than the traditional methods. Finally, examples are given to show the advantages and effectiveness of the results.

Finite-time synchronization of Markovian jump complex networks with generally uncertain transition rates

In this paper, finite-time synchronization for a class of Markovian jump complex networks (MJCNs) with generally uncertain transition rates (GUTRs) is considered. In this GUTR network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model is more general than partly unknown transition rates (PUTRs). By constructing a suitable stochastic Lyapunov–Krasovskii function, using finite-time stability theorem and pinning control approaches, a sufficient finite-time synchronization criterion is derived in term of linear matrix inequalities (LMIs), which is easy to solve with the help of the LMI toolbox in Matlab. Finally, theoretical results are supported by numerical simulations.

Exponential synchronization of delayed Markovian jump complex networks with generally uncertain transition rates

This paper investigates the exponential synchronization problem for a class of Markovian jump complex networks(MJCNs) with generally uncertain transition rates(GUTRs). In this GUTR neural network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model could be applied to many practical cases. Based on the Lyapunov functional method and Kronecker product technique, a sufficient condition on the exponentially synchronization in mean square is derived in terms of linear matrix inequalities (LMIs)-which can be easily solved by using the Matlab LMI toolbox. Finally, one numerical example is well-studied to illustrate the effectiveness of the developed method.

An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

This paper is concerned with the problem of robust H∞ control for a class of singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs) and actuator saturation via anti-windup design. In this GUTR model, each transition rate can be completely unknown or only its estimate value is known. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilize the SMJSs in the absence of actuator saturation, anti-windup compensators are designed to impair the actuator saturation effect on the closed-loop systems subject to admissible external disturbances, Itô-type stochastic disturbances, transition rate and norm-bounded parameter uncertainties. Anti-windup compensation gains can be derived via solving a convex optimization problem with constraints of a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.

A sliding mode approach to robust stabilisation of Markovian jump linear time-delay systems with generally incomplete transition rates

This paper is devoted to investigating the problem of robust sliding mode control for a class of uncertain Markovian jump linear time-delay systems with generally uncertain transition rates (GUTRs). In this GUTR model, each transition rate can be completely unknown or only its estimate value is known. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. A sliding mode control law is developed to drive the state trajectory of the closed-loop system to the specified linear switching surface in a finite-time interval in spite of the existing uncertainties, time delays and unknown transition rates. Finally, an example is presented to verify the validity of the proposed method.

Robust Stabilization of Markovian Jump Linear Singular Systems with Wiener Process and Generally Incomplete Transition Rates

This paper is devoted to the investigation of robust stability and robust stabilizability for a class of uncertain Markovian jump continuous-time singular systems with Wiener process and generally uncertain transition rates (GUTRs). This new uncertain model is more general than the existing ones and can be applicable to more practical situations because of its uncertain parameters and transition rates. Each transition rate can be completely unknown, or only its estimate value is known. Our interests are focused on establishing sufficient criteria on robust stability and the design of a state feedback controller such that the robust stochastic stability is guaranteed, even if the singular system incorporates GUTRs, Wiener process disturbance and norm-bounded uncertainties. These sufficient criteria are derived in terms of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.

Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability

The problem of global exponential stability in mean square of delayed Markovian jump fuzzy cellular neural networks (DMJFCNNs) with generally uncertain transition rates (GUTRs) is investigated in this paper. In this GUTR neural network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model is more general than the existing ones. By constructing suitable Lyapunov functionals, several sufficient conditions on the exponential stability in mean square of its equilibrium solution are derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness and efficiency of our results.

Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates

This note is devoted to investigating the stability and stabilization problems for continuous-time singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). In this GUTR singular model, each transition rate can be completely unknown or only its estimate value is known. In terms of a set of coupled linear matrix inequalities (LMIs), a sufficient condition is established to ensure the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent state-feedback controller is derived to guarantee the closed-loop systems stochastically admissible by applying the LMI technique. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method.

Stabilisation of mode-dependent singular Markovian jump systems with generally uncertain transition rates

This paper is devoted to investigating the stability and stabilisation problems for continuous-time mode-dependent singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). First, we establish a sufficient condition in terms of a set of coupled linear matrix inequalities (LMIs) to ensure the systems to be regular, impulse-free and stochastically stable. Then, we design a mode-dependent state-feedback controller to guarantee the closed-loop systems stochastically admissible by applying the LMI technique. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method.

Quantized State-Feedback Stabilization for Delayed Markovian Jump Linear Systems with Generally Incomplete Transition Rates

This paper is concerned with the robust quantized state-feedback controller design problem for a class of continuous-time Markovian jump linear uncertain systems with general uncertain transition rates and input quantization. The uncertainties under consideration emerge in both system parameters and mode transition rates. This new uncertain model is more general than the existing ones and can be applicable to more practical situations because each transition rate can be completely unknown or only its estimate value is known. Based on linear matrix inequalities, the quantized state-feedback controller is formulated to ensure the closed-loop system is stable in mean square. Finally, a numerical example is presented to verify the validity of the developed theoretical results.

Stability of Markovian jump systems with generally uncertain transition rates

This paper is concerned with exploring stability analysis for a class of Markovian jump systems (MJSs) with generally uncertain transition rates (GUTRs). In the GUTR model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model is more general than the existing ones and can be applicable to more practical situations. The stability criterion for such a class of uncertain MJSs is derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed method.