Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities

This paper addresses the problem of the delay-dependent stability for neutral Markovian jump systems with partial information on transition probability. The time delays discussed in this paper are time-varying delays. Combined the new constructed Lyapunov functional with the introduced free matrices, and using the analysis technique of matrix inequalities, the delay-dependent stability conditions are obtained. The obtained results are formulated in terms of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Three numerical examples are given to show the validity and potential of the developed criteria.     

Reliable control for event-triggered singular Markov jump systems with partly unknown transition probabilities and actuator faults

In this paper, the problem of reliable controller design for event-triggered singular Markov jump systems with partly known transition probabilities, nonlinear perturbations and actuator faults is studied. To mitigate the burden of data transmissions over network, two event-triggered schemes with different triggering conditions are introduced. The switch law between the two event-triggered schemes is governed by a random variable with Bernoulli distribution. Taking nonlinear perturbations and actuator faults into account, the resulting closed-loop system is converted into a time-delay singular Markov jump system with partly known transition probabilities. Sufficient conditions of stochastically admissible for the resulting closed-loop system are obtained in terms of a group of linear matrix inequalities. The co-design of desirable reliable controller and weighting matrices of event-triggered schemes is presented. Finally, two numerical examples are given to show the effectiveness of the developed results.     

Robust control for Markovian jump systems with partially known transition probabilities and nonlinearities

This paper investigates robust _H∞$H_{\infty }$ controller design for Markovian jump systems (MJSs) with partially known transition probabilities (TPs) and nonlinearities. A general nonlinearity model is proposed, the generalization lies in three aspects: (1) the nonlinearities include both state and delayed state information; (2) the nonlinearities satisfy sector-bounded conditions; (3) apart from the lower and upper bounds, the probability information of the nonlinearities belonging to different sector bounds is utilized. The MJSs are considered with some of the TPs completely unknown, which can cover the MJSs with completely known TPs and completely unknown TPs as special cases. It should be noted that the relationship between known and unknown TPs is utilized, which can reduce the conservatism of the results. By using the Lyapunov functional method, sufficient conditions are derived. At last, two simulation examples show the application and effectiveness of the proposed method.     

Nonquadratic stabilization conditions for nonhomogeneous Markovian jump fuzzy systems with higher-level operation modes

This paper is concerned with the problem of designing a dissipative control for generalized nonhomogeneous Markovian jump fuzzy systems (MJFSs) that can cover both piecewise-homogeneous MJFSs and nonhomogeneous MJFSs through the use of dual modes, i.e., plant and higher-level modes. Based on a dual-mode-dependent fuzzy control law within a nonparallel distributed compensation (non-PDC) scheme, the nonquadratic stabilization conditions are first formulated in terms of multi-parameterized linear matrix inequalities (M-PLMIs), and then be transformed into a finite set of solvable LMIs without reducing M-PLMIs to PLMIs. Further, since the proposed relaxation technique can address the transition probabilities of plant and higher-level modes at once, the characteristics on mutual dependence between dual modes are fully incorporated into the nonquadratic stabilization conditions. Two illustrative examples are given to show the validity of the proposed approach.     

Controller synthesis for Markovian jump systems with incomplete knowledge of transition probabilities and actuator saturation

This paper is concerned with Markovian jump systems subject to incomplete knowledge of transition probabilities and actuator saturation. The system under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities. By introducing some free-connection weighting matrices to handle the inaccessible elements of transition probabilities, a new criterion is 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, two numerical examples are provided to illustrate the merits of our method.     

Improved asynchronous stabilization method for nonhomogeneous Markovian jump fuzzy systems with incomplete transition rates

This paper proposes an improved asynchronous stabilization method for nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition rates via a nonparallel distributed compensation (non-PDC) control scheme. To cover a more realistic situation in the continuous-time MJFS domain, this paper focuses on addressing the following issues differently from previous studies: 1) emergence of a nonhomogeneous Markov process and asynchronous control mode, 2) separation of the Lyapunov matrix from the control gain within stabilization conditions, and 3) relaxation of stabilization conditions subject to multiple time-varying parameters. Specifically, the effects of nonhomogeneity and asynchronism are simultaneously reflected in the stabilization conditions, and separation and relaxation techniques are additionally developed as needed. Finally, the advantages of our method are illustrated through two examples: the first is provided to show the effectiveness of the proposed separation technique, and the second is provided to show that the relaxed stabilization conditions are less conservative than previous results.     

Sampled-data predictive control for uncertain jump systems with partly unknown jump rates and time-varying delay

This paper presents a sampled-data predictive control strategy for a class of uncertain continuous-time Markovian jump linear system (MJLS) with time-varying delay. The system under consideration covers MJLS with completely known jump rates and arbitrary switched linear system. The predictive formulation utilizes both off-line and on-line optimization paradigms. The feasibility of the control scheme and the stability of the closed-loop system are investigated by introducing a modified stochastic invariant ellipsoid. The conditions for the existence of a stabilizing optimal controller for the underlying system are obtained via the semi-definite programming (SDP). A numerical example is given to verify efficiency and potential of the developed approach.     

Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates

In this paper, finite-time synchronization problem is considered for a class of Markovian jump complex networks (MJCNs) with partially unknown transition rates. By constructing the suitable stochastic Lyapunov–Krasovskii functional, using finite-time stability theorem, inequality techniques and the pinning control technique, several sufficient criteria have been proposed to ensure the finite-time synchronization for the MJCNs with or without time delays. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, this paper has important theory significance and practical application value. Finally, numerical simulations illustrated by mode jumping from one mode to another according to a Markovian chain with partially unknown transition probability verify the effectiveness of the proposed results.     

Bayesian estimation for jump Markov linear systems with non-homogeneous transition probabilities

This paper considers the state estimation problem for a class of discrete-time non-homogeneous jump Markov linear systems (JMLSs), where the transition probability matrix (TPM) is assumed to be time-variant and takes value in a finite set randomly at each time step. To show the simplicity brought by the finite-valued hypothesis, the optimal recursion for the posterior TPM probability density functions conditioned on that the TPM belongs to a continuous set is firstly derived. Then, we naturally incorporate the proposed TPM estimation into the recursion of system state. Two interacting multiple-model (IMM)-type approximation stages are employed to avoid the exponential computational requirements. The resulting filter reduces to the IMM filter when the number of candidate TPMs is unity. A meaningful example is presented to illustrate the effectiveness of our method.     

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.     

Necessary and sufficient criteria for asynchronous stabilization of Markovian jump systems

This paper is concerned with asynchronous stabilization for a class of discrete-time Markovian jump systems. The mode of designed controller is considered to be not perfectly synchronous with the activated mode of the Markovian jump system. In order to achieve the asymptotic stability with asynchronous controller, a conditional probability is introduced to describe the asynchronism of system and controller modes, which is dependent on the active system mode. Besides, due to the difficulty in acquiring all the mode transition probabilities in practice, the transition probabilities of the Markovian jump system and the controllers are supposed to be partially unknown. A necessary and sufficient condition is developed to guarantee the stochastic stability of the resultant closed-loop system and further extended to asynchronous stabilization with partially known transition probabilities. Finally, the effectiveness and advantages of the proposed methods are demonstrated by two illustrative examples.     

Resilient control based on disturbance observer for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters

In this paper, the composite anti-disturbance resilient control is considered for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters under multiple disturbances. Three kinds of disturbances are included in the studied system. One is generated by an external system and it enters the hybrid system from the channel of the control input. The other one is stochastic white noise. And the third one is the external unknown time-varying disturbance and it is supposed to be H₂ norm bounded. By combining the disturbance-observer-based-control scheme, H_∞ control technique and resilient control method, a composite anti-disturbance resilient controller is constructed to attenuate and eliminate the affection of these disturbances, and ensures the whole closed-loop system regular, impulse free and stochastically stable with the corresponding control performance. Then, some sufficient conditions and the gains of the controller and observer are obtained by using Lyapunov function method and the linear matrix inequalities (LMIs) technique. Finally, two numerical examples are given to show the effectiveness of presented method.     

Intermittent stochastic stabilization of Markovian jump systems via sampled data

This paper is concerned with stochastic stabilization of Markovian jump systems. By using some novel analysis technique, especially the established quasi time-homogeneous property, the aperiodic intermittent and sampled-data strategies have been integrated into stochastic stabilized theory. A criterion is derived, which ensures the stabilization via the aperiodic intermittent stochastic feedback based on sampled-data of state and mode of Markovian jump systems. Two numericalexamples are given to show the effectiveness of our criterion.     

Stochastic stabilization of Markovian jump neutral systems with fractional Brownian motion and quantized controller

This paper explores the delay dependent stochastic stabilization of Markovian jump neutral systems (MJNS) which are modeled by fractional Brownian motion(fBm) via a quantized controller. A function Round quantizer is introduced which solves the model uncertainties and the nonlinear part by a uniform operator. Then by structuring a Lyapunov–Krasovskii functional (LKF) and the aid of linear matrix inequalities (LMIs) method, a stochastic stability criterion is achieved. Last, different parameters are selected to simulate the effectiveness of our findings.