Incomplete Transition Rates Research Articles

Exponential Stability of Neutral-Type Impulsive Markovian Jump Neural Networks with General Incomplete Transition Rates

This paper is devoted to the investigation of exponential stability of Neutral-type impulsive Markovian jump neural networks with mixed time-varying delays and generally uncertain transition rates (GUTRs). Each transition rate can be completely unknown or only its estimate value is known in this GUTR model. This new uncertain model is more general than the existing ones. By utilizing Lyapunov–Krasovkii functional approach and linear matrix inequality technology, some novel globally exponentially stable results are derived. An example is given to show the effectiveness of the obtained results.

Cluster and local mode‐dependent filtering for distributed Markovian jump systems in lossy multi‐sensor networks

This study addresses an H ∞ filtering problem for distributed Markovian jump systems (DMJSs) in multi-sensor networks with inaccessible global jumping modes, random data losses, random sensing topologies and incomplete mode transition rates (TRs). First, locally overlapped clusters are introduced to reformulate the DMJS to account for the scenario that the global modes of the DMJS are not accessible for filter design. Second, a new cluster and local mode-dependent H ∞ filtering framework is presented to incorporate the simultaneous presence of Markovian data losses and sensing topologies as well as incomplete mode TRs. The proposed H ∞ filters depend on only available information of cluster modes and local modes within this cluster, and thus eliminating the requirement of complete global modes. Third, criteria for designing desired filters are derived to preserve the stochastic stability of the resulting filtering error system under a prescribed H ∞ performance index. The proposed results are shown to be more general by covering some existing results as special cases. Finally, an F404 aircraft engine system is employed to demonstrate the effectiveness of the proposed filter design approach.

Quantized control for uncertain singular Markovian jump linear systems with general incomplete transition rates

Quantization is indeed a natural way to take into consideration in the control design of the complexity constraints for the controller as well as the communication constraints in the information exchange between the controller and the plant. This paper is devoted to investigating quantized state-feedback control problems for a class of continuous-time uncertain singular Markovian jump linear systems (CUSMJLSs) with generally uncertain transition rates (GUTRs) and input quantization. In this case, each transition rate can be completely unknown or only its estimate value is known. First, input quantization is introduced, then by introducing new matrix inequality conditions, sufficient conditions are formulated for quantized state-feedback control of CSMJLUSs with GUTRs and input quantization. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed results.

Positive observer design for positive Markovian jump systems with mode-dependent time-varying delays and incomplete transition rates

The paper is concerned with positive observer design for positive Markovian jump systems with incomplete transition rates and time delays that are mode-dependent and time-varying. Firstly, by applying an appropriate co-positive type Lyapunov-Krasovskii function and free-connection weighting vectors, sufficient conditions are proposed to ensure stochastic stability of the error positive system and existence of the positive observer. All the proposed conditions are derived in linear programming. Finally, an example is given to demonstrate the validity of the main results.

Positive L1-gain filter design for positive Markovian jump systems with time-varying delay and incomplete transition rates

This paper deals with the problem of positive L1-gain filter design for positive Markovian jump systems with time-varying delay and incomplete transition rates. By implying an appropriate co-positive type Lyapunov function and free-connection weighting vectors, sufficient conditions for stochastic stability of the filtering error system are established. Then, the L1-gain performance is analyzed. Based on the obtained results, a positive full-order filter is designed to ensure that the corresponding filtering error system is positive and stochastically stable with L1-gain performance. All the conditions are derived in linear programming. Finally, the obtained theoretical results are demonstrated by a numerical example.

Passivity and passification for stochastic Markovian jump systems with incomplete transition rates and actuator saturation

This paper deals with the problem of passivity and passification for stochastic Markovian jump systems with incomplete transition rates and actuator saturation. By use of the polytopic model, sufficient conditions are built such that the closed-loop constrained system is stochastically passive. The procedure of deriving a state feedback controller is converted into an optimization problem with a set of linear matrix inequalities. Finally, the simulation results of a linearized dynamic model of a vertical take-off and landing aircraft in the vertical plane illustrate the effectiveness of the proposed schemes.

Sliding mode control of Markovian jump systems with incomplete information on time-varying delays and transition rates

This paper is concerned with robust sliding mode control (SMC) for continuous-time Markovian jump delay systems with incomplete transition rates (TRs), the time-varying delays are unclear and just bounded sometimes. Two methods are employed to investigate this control issue. One is movement decomposition method by which reduced-order sliding mode dynamics is obtained; the other is via sliding mode observer and full-order sliding mode dynamics is obtained on the estimation space. In both cases, sufficient conditions are established in terms of a set of coupled linear matrix inequalities (LMIs) to ensure the sliding mode dynamics to be mean-square exponentially stable; moreover, novel sliding mode controllers, which need not full knowledge on time-varying delays, are synthesized to guarantee the reachability of the prescribed sliding surface. Finally, numerical examples are provided to illustrate the effectiveness of the proposed methods.

Finite-time guaranteed cost control for Itô Stochastic Markovian jump systems with incomplete transition rates

Summary This paper is concerned with the finite-time guaranteed cost control problem for stochastic Markovian jump systems with incomplete transition rates. By a mode-dependent approach (MDA), several new sufficient conditions for the existence of state and output feedback finite-time guaranteed cost controllers are provided, and the upper bound of cost function is more accurately expressed. Moreover, these results' superiorities are analyzed and shown. A new N-mode optimization algorithm is given to minimize the upper bound of cost function. Finally, a detailed example is utilized to demonstrate the merit of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.

Sampled-Data Synchronization Analysis of Markovian Neural Networks With Generally Incomplete Transition Rates.

This paper investigates the problem of sampled-data synchronization for Markovian neural networks with generally incomplete transition rates. Different from traditional Markovian neural networks, each transition rate can be completely unknown or only its estimate value is known in this paper. Compared with most of existing Markovian neural networks, our model is more practical because the transition rates in Markovian processes are difficult to precisely acquire due to the limitations of equipment and the influence of uncertain factors. In addition, the time-dependent Lyapunov-Krasovskii functional is proposed to synchronize drive system and response system. By applying an extended Jensen's integral inequality and Wirtinger's inequality, new delay-dependent synchronization criteria are obtained, which fully utilize the upper bound of variable sampling interval and the sawtooth structure information of varying input delay. Moreover, the desired sampled-data controllers are obtained. Finally, two examples are provided to illustrate the effectiveness 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.

Model Predictive Control for Continuous-Time Singular Jump Systems with Incomplete Transition Rates

This paper is concerned with model predictive control (MPC) problem for continuous-time Markov Jump Systems (MJSs) with incomplete transition rates and singular character. Sufficient conditions for the existence of a model predictive controller, which could optimize a quadratic cost function and guarantee that the system is piecewise regular, impulse-free, and mean square stable, are given in two cases at each sampling time. Since the MPC strategy is aggregated into continuous-time singular MJSs, a discrete-time controller is employed to deal with a continuous-time plant and the cost function not only refers to the singularity but also considers the sampling period. Moreover, the feasibility of the MPC scheme and the mean square admissibility of the closed-loop system are deeply discussed by using the invariant ellipsoid. Finally, a numerical example is given to illustrate the main results.

Robust Finite-Time Output Feedback $$ H_\infty $$ H ∞ Control for Stochastic Jump Systems with Incomplete Transition Rates

This article aims to investigate the problem of robust finite-time output feedback $$ H_\infty $$H? control for stochastic jump systems with incomplete transition rates. Firstly, for the nominal stochastic jump systems, the sufficient conditions for the finite-time boundedness and finite-time output feedback stabilization are developed, respectively. Then, a robust finite-time $$ H_\infty $$H? output feedback controller is designed by means of linear matrix inequalities. A key point of this work is to relax the special requirement of completely known transition rates to more general form that mixes two cases of completely known and completely unknown transition rates. Finally, a numerical example is given to demonstrate the applicability of the main results.

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 Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

The delay‐dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov‐Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided.