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1.
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.  相似文献   

2.
This paper considers a stability analysis problem for continuous-time Markovian jump linear systems under aperiodic samplings which are represented as Markovian jump linear systems with input delay. For the systems, this paper constructs a Lyapunov functional by utilizing a fragmented-delay state, which is defined between the last sampling instant and the present time, and a new state space model of the fragmented state. Based on the Lyapunov functional, a stability criterion is derived in terms of linear matrix inequalities by using reciprocally convex approach and integral inequality. Here, the reciprocally convex approach and integral inequality are associated not only with the current state, the delayed state, and the maximum-admissible delay state, but also with the fragmented-delay state. The simulation result shows the effectiveness of the proposed stability criterion.  相似文献   

3.
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.  相似文献   

4.
This paper presents an adaptive event-triggered filter of positive Markovian jump systems based on disturbance observer. A new adaptive event-triggering mechanism is constructed for the systems. A positive disturbance observer is designed for the systems to estimate the disturbance. A distributed output model of each subsystem of positive Markovian jump systems is introduced. Then, an adaptive event-triggering distributed filter is designed by employing stochastic copositive Lyapunov functions. All presented conditions are solvable in terms of linear programming. Under the designed disturbance observer and the distributed filter, the corresponding error system is stochastically stable. The filter design approach is also developed for discrete-time positive Markovian jump systems. The contribution of the paper lies in that: (i) A new adaptive event-triggering mechanism is established for positive systems, (ii) A positive disturbance observer is designed for the disturbance of positive Markovian jump systems, and (iii) The designed distributed filter can guarantee the stochastic stability of the error while existing filters in literature only achieve the stochastic gain stability of the error. Finally, two examples are given to illustrate the effectiveness of the proposed design.  相似文献   

5.
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.  相似文献   

6.
This paper deals with the input–output finite-time stabilization problem for Markovian jump systems (MJSs) with incompletely known transition rates. An observer-based output feedback controller is constructed to study the input–output finite-time stability (IO-FTS) problem. By using the mode-dependent Lyapunov–krasovskii functional method, a sufficient criterion checking the IO-FTS problem is provided. Then, an observer and a corresponding state feedback controller for the individual subsystem are respectively designed to solve the input–output finite-time stabilization problem for the systems. Finally, a numerical example on the mass-spring system model is investigated to bring out the advantages of the control scheme proposed in this paper.  相似文献   

7.
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.  相似文献   

8.
This paper is concerned with stability for aperiodic sampled-data systems. Firstly, for aperiodic sampled-data systems without uncertainties, a new Lyapunov-like functional is constructed by introducing the double integral of the derivative of the state, the integral of the state, and the integral of the cross term of the state and the sampled state. When estimating the derivative of the Lyapunov-like functional, superior integral inequalities to Jensen inequality are employed to get a tighter upper bound. By the Lyapunov-like functional principle, sampling-interval-dependent stability results are derived. Then, the stability results are extended to aperiodic sampled-data systems with polytopic uncertainties. Finally, some examples are listed to show the stability results have less conservatism than some existing ones.  相似文献   

9.
This paper investigates the problem of stochastic stability and stabilization of stochastic Markovian jump delay systems (SMJDSs) based on LaSalle theorem. The time delays are assumed to be time-varying and numerous stochastic disturbances are considered. Attention is focused on the design of the mode-dependent state feedback controller for SMJDSs based on LaSalle theorem such that the closed-loop SMJDSs are almost surely asymptotically stable. The sufficient conditions for the solvability of the state feedback control problem are obtained in terms of linear matrix inequalities (LMIs). When the LMIs are feasible, the desired state feedback controller is also given. Two numerical examples including the vertical take-off and landing (VTOL) helicopter system are employed to demonstrate the effectiveness and usefulness of the method proposed in this paper  相似文献   

10.
This paper is concerned with master-slave synchronization for chaotic Lur'e systems subject to aperiodic sampled-data. To reduce the communication burden, an aperiodic event-triggered (APET) transmission scheme is introduced to determine the transmission of the latest sampling synchronization data. In order to reduce the design conservatism, a novel time-dependent Lyapunov functional (TDLF) is constructed to fully use the characteristics about sampling behavior, triggering error, and nonlinear part of the system, simultaneously. A more relaxed constraint criterion is then presented to ensure the positivity of the whole functional between two sampling instants. By partially resorting to the TDLF, the APET-based synchronization criterion depending on the upper and lower bounds of the uncertain sampling period is presented. The synchronization criterion based on aperiodic-sampling mechanism is also provided. Finally, a typical example about neural networks is offered to illustrate the benefit and validity of obtained synchronization methodologies.  相似文献   

11.
This paper discusses the stabilization criteria for stochastic neural networks of neutral type with both Markovian jump parameters. First, delay-dependent conditions to guarantee the globally exponential stability in mean square and almost surely exponential stability of such systems are obtained by combining an appropriate constructed Lyapunov–Krasovskii functional with the semi-martingale convergence theorem. These conditions are in terms of the linear matrix inequalities (LMIs), which can be some less conservative than some existing results. Second, based on the obtained stability conditions, the state feedback controller is designed. Finally, four numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.  相似文献   

12.
This paper investigates the design problem of asynchronous output feedback controller via sliding mode for a class of discrete-time fuzzy Markovian jump systems. Considering the non-synchronization phenomenon between the Markovian jump systems and the sliding controller, an asynchronous control method with a stochastic variable is adopted to describe the connections of the systems and controller. On the other hand, not full of states are accessible for the controller since it is impossible or very expensive to estimate all of states, while the output information can be acquired to the controller all the time. Based on the above aspects, the asynchronous output feedback controller via sliding mode for fuzzy Markovian jump systems is investigated to ensure the sliding mode dynamics to be stochastically stable, besides, several sufficient conditions are given to find a set of feasible solutions of the controller parameters. The asynchronous sliding mode control law is synthesized to guarantee the reachability of the trajectories of the closed-loop systems. Finally, a simulation example is to verify the effectiveness of the control strategy.  相似文献   

13.
This paper investigates sliding mode control of stochastic singular Markovian jump systems with nonlinearity. The unmatched nonlinearity satisfies one-sided Lipschitz condition and quadratically inner-boundedness. In term of a new technical variable transformation, sufficient conditions are developed for nonlinear stochastic singular Markovian jump systems constrained on sliding manifold to guarantee stochastic admissibility and uniqueness of solution based on implicit function theorem. The sliding mode control law by which the trajectories of system can be compelled to the predefined sliding surface in finite time no matter what initial state value is, is synthesized. The derivative singular matrix is fully considered in the whole design process such that the derived conditions can be checked easily.The technical treatment of the nonlinear matrix term avoids the classification discussion of sliding mode controller design. Convex optimization problems subject to linear matrix inequalities are formulated to optimize the desired indexes of interest. Finally, the effectiveness of the proposed approach is illustrated by a numerical example and a practical example.  相似文献   

14.
This paper studies the global sampled-data output feedback stabilization problem for a class of stochastic nonlinear systems. The considered system is in non-strict feedback form with unknown time-varying delay. A state observer is introduced to estimate the unmeasured states. With the help of the backstepping method, a linear sampled-data output feedback controller is constructed. By choosing an appropriate Lyapunov–Krasoviskii functional and an allowable sampling period, it is shown that the stochastic system can be globally asymptotically stabilized in the mean square sense under the developed control scheme. Finally, two examples are presented to verify the effectiveness of the designed control scheme.  相似文献   

15.
This paper presents new parameterized sampled-data stabilization criteria using affine transformed membership functions for T-S fuzzy systems. To deal with the sampled control input having aperiodic sampling intervals, the proposed method adopts new looped functionals, and employs a modified free weighting matrix inequality. A relaxed condition for the controller design is derived by formulating the constraint conditions of the membership functions in the proposed controller with affinely matched weighting parameter vectors. Based on a newly devised lemma for handling affinely matched vectors, the stabilization and guaranteed cost performance criteria are given in terms of linear matrix inequalities (LMIs). The superiority of the presented method is demonstrated via significantly improved results in numerical examples.  相似文献   

16.
This paper studies the stochastic stability problem for Markovian jump systems with unified uncertain transition rates via multiple integral techniques. The considered transition rates unify some existing ones in a framework, which are more general and practical. A multiple-integral-type Lyapunov–Krasovskii functional (MITLKF) is constructed, which contains more ply of integral terms than some existing ones. In order to obtain a tighter bound of the MITLKF, an auxiliary function-based multiple integral inequality (AFMII) is proposed, which encompasses some existing ones as its special cases. Based on these ingredients, a novel stability condition is derived for Markovian jump systems with the unified uncertain transition rates. The effectiveness of the proposed approach is demonstrated by two examples.  相似文献   

17.
This work is concerned with the finite-time sliding mode control for a class of Markovian jump systems subject to actuator nonlinearities, where the elements in the transition rate matrix are uncertain or even completely unknown. A suitable sliding mode controller is designed such that the finite-time stochastic boundedness of state trajectories is attained during a given finite-time interval, in which two different robust terms are introduced for the known and unknown modes to deal with the effect of uncertain transition rates. Moreover, the connections among sliding functions under Markovian jumping for SMC systems are analyzed. Finally, some simulation results with a wheeled mobile manipulator are provided.  相似文献   

18.
This paper addresses the stabilization of stochastic jump diffusion system in both almost sure and mean square sense by state-feedback control. We find conditions under which the solutions to the class of jump-diffusion process are mean square exponentially stable and almost sure exponentially stable. We investigate the stabilization of the stochastic jump diffusion systems by applying the state-feedback controllers not only in the drift term, but also in jump diffusion terms. Meanwhile our theory is generalized to cope with the uncertainty of system parameters. All the results are expressed in terms of linear matrix inequalities (LMIs), which are easy to be checked in a MATLAB Toolbox.  相似文献   

19.
In this paper, the problems of stochastic finite-time stability and stabilization of discrete-time positive Markov jump systems are investigated. To deal with time-varying delays and switching transition probability (STP), stochastic finite-time stability conditions are established under mode-dependent average dwell time (MDADT) switching signal by developing a stochastic copositive Lyapunov-Krasovskii functional approach. Then a dual-mode dependent output feedback controller is designed, thus stochastic finite-time stabilization is achieved based on linear programming technique. Finally, two examples are given to show the effectiveness of our results.  相似文献   

20.
This paper studies the problem of continuous gain-scheduled PI tracking control on a class of stochastic nonlinear systems subject to partially known jump probabilities and time-varying delays. First, gradient linearization procedure is used to construct model-based linear stochastic systems in the vicinity of selected operating states. Next, based on stochastic Lyapunov stabilization analysis, sufficient conditions for the existence of a PI tracking control are established for each linear model in terms of linear matrix inequalities. Finally, continuous gain-scheduled approach is employed to design continuous nonlinear PI tracking controllers on the entire nonlinear jump system. Simulation example is given to illustrate the effectiveness of the developed design techniques.  相似文献   

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