Singular Markov Research Articles

Observer-based control for singular Markov jump systems with actuator saturation and time-varying transition rates

This paper investigates the issue of observer-based control for singular Markov jump systems (SMJSs) with time-varying delay, actuator saturation and time-varying transition rates. Firstly, the state feedback controller is proposed, which based on the state observer. The time-varying transition rates are quantized by the logarithmic quantizer. In addition, the appropriate Lyapunov function is considered to ensure that the original system and the error system are singular stochastic admissible (SSA) with mixed H∞ and passivity performance. Finally, four examples are provided to expound the consistency of the technique.

Asynchronous passive dynamic event‐triggered controller design for singular Markov jump systems with general transition rates under stochastic cyber‐attacks

This study focuses on the issue of asynchronous passive controller design for singular Markov jump systems with general transition rates under stochastic cyber-attacks. To maximise the utilisation of network resources by reducing unnecessary data transmissions, a dynamic event-triggered rule is properly presented. Assuming that the system might be attacked by two kinds of stochastic cyber-attacks, which are governed by two different functions. The asynchronous fact between the modes of the system and controller is described by the hidden Markov model. The criterion of stochastically admissible with a certain passive performance is established. In the light of a series of linear matrix inequalities, the asynchronous controller and dynamic event-triggered rule are designed simultaneously. A numerical instance under different event-triggered rules is offered to reveal the usefulness and effectiveness of the developed method.

Robust fault detection of singular Markov jump systems with partially unknown information

The problem of robust fault detection for singular Markov jump systems with partially unknown transition probabilities is investigated in the paper. A fault detection observer is designed such that the residual signal is sensitive to fault signals and robust to unknown disturbances. By using Lyapunov function approach, sufficient conditions under which the system is stochastic stable with robustness and sensitiveness are given. Furthermore, an optimization problem is also derived. A simulation example is given to show the effectiveness.

Synchronization of Singular Markovian Jumping Neutral Complex Dynamical Networks with Time-Varying Delays via Pinning Control

This article discusses the synchronization problem of singular neutral complex dynamical networks (SNCDN) with distributed delay and Markovian jump parameters via pinning control. Pinning control strategies are designed to make the singular neutral complex networks synchronized. Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities based on a modified Lyapunov-Krasovskii functional approach. By applying the Lyapunov stability theory, Jensen’s inequality, Schur complement, and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the stability of the system. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.

Stochastic admissibility of singular Markov jump systems with time-delay via sliding mode approach

In this article, stochastic admissibility of singular Markov jumping systems (SMJSs) with time-varying delays is studied by sliding mo de control (SMC) method. Firstly, we construct integral-type sliding mode switching functions for each Markov jump subsystem, next, we construct some linear matrix inequalities(LMI) and sufficient conditions for stochastic admissibility are given. Then the sliding mo de controller and switching rules are designed by Lyapunov stability method, the state trajectory can reach the sliding mode surface (SMS) in a limited time, resulting in stable sliding mode dynamics. Finally, two examples are given to illustrate the effectiveness and feasibility of the proposed scheme.

Fault Detection Filter Design of Polytopic Uncertain Continuous-Time Singular Markovian Jump Systems with Time-Varying Delays

This paper investigates the problem of full-order and reduced-order fault detection filter (FDF) design under unified linear matrix inequality (LMI) conditions for a class of continuous-time singular Markovian jump systems (CTSMJSs) with time-varying delays and polytopic uncertain transition rates. By constructing a new Lyapunov function, sufficient conditions are firstly provided for the singular model error augmented system such that the system is stochastically admissible with an H∞ performance level γ. And then, by applying a novel convex polyhedron technique to decoupled linear matrix inequalities, the full-order and reduced-order fault detection filter parameters can be obtained within a convex optimization frame. The reduced-order fault detection filter (FDF) can not only meet the fault detection accuracy requirements of complex systems but also improve the fault detection efficiency. Finally, a DC motor and an illustrative simulation example are given to verify the feasibility and effectiveness of the proposed algorithms.

Dynamic event-based finite-time mixed [formula omitted] and passive asynchronous filtering for T–S fuzzy singular Markov jump systems with general transition rates

In this paper, the design of finite-time mixed H∞ and passive asynchronous filter for T–S fuzzy singular Markov jump systems with general transition rates under the dynamic event-based scheme is discussed. An asynchronous filter is considered such that the phenomena of asynchronous modes between the original singular Markov jump systems and the considered filter is modelled as a hidden Markov model. A dynamic event-based scheme is proposed to further mitigate the network transmission burden. By augmenting the states of the original singular Markov jump systems and the constructed asynchronous filter, the filtering error system is transformed into a singular time-delay Markov jump system. Based on the Lyapunov–Krasovskii functional concerning the internal dynamic variable, the criteria of stochastically admissible and stochastically finite-time boundness with the given mixed H∞ and passivity performance index for the filtering error system are subject to linear matrix inequalities and several constraint conditions. Furthermore, the unified co-design approach of the desired asynchronous filter and the proposed dynamic event-based strategy is developed. Finally, a numerical instance is employed to demonstrate the correctness and effectiveness of the developed technique.

A dynamic event-triggered H∞ control for singular Markov jump systems with redundant channels

ABSTRACTIn this paper, the problem of asynchronous control for singular Markov jump systems with redundant channels under the dynamic event-triggered scheme is studied. To save the resource of bandwidth limited network, a dynamic event-triggered scheme is proposed. The technique of redundant channels is employed to improve the successful rate of the communication network, which are modelled as two mutually independent Bernoulli-distributed random variables. A hidden Markov model is proposed to formulate the asynchronisation phenomena between the system modes and the controller modes, which results in the fact that the closed-loop system is a singular hidden Markov jump system. The criteria of regular, causal and stochastically stable with a certain performance for the closed-loop system are obtained. The co-design of asynchronous controllers and the dynamic event-triggered scheme is proposed in terms of a group of feasible linear matrix inequalities. A numerical example and a practical example are presented to show the effectiveness of the developed method.

Event-based asynchronous dissipative filtering for T–S fuzzy singular Markovian jump systems with redundant channels

In this paper, the issue of asynchronous dissipative filter design for a class of Takagi–Sugeno (T–S) fuzzy singular Markov jump systems (SMJSs) with redundant channels under the event-triggered scheme is investigated. The event-triggered scheme, the technique of redundant channels are adopted to relieve the total number of data transmission and improve the transmission quality over the network, respectively. The hidden Markov model (HMM) is utilized to describe the phenomena of asynchronous modes between the original system and the designed filter. Based on the stochastic Lyapunov functional and the method of free-weighting matrices, sufficient conditions of stochastically admissible and strictly dissipative for the filtering error system are developed concerning a set of linear matrix inequalities (LMIs). The co-design of asynchronous filter and the weighting matrices of the event-triggered scheme is determined by the feasible LMIs. Finally, a numerical example is presented to show the usefulness and effectiveness of the proposed method.

Observer‐based mode‐independent integral sliding mode controller design for phase‐type semi‐Markov jump singular systems

SummaryThis paper considers the observer‐based integral sliding mode controller design problem of semi‐Markovian jumping singular systems with time‐varying delays. Firstly, by using a plant transformation and supplementary variable technique in the work of Hou et al, the discussed phase‐type semi‐Markov jump singular system is equivalently transformed into its associated Markov jump singular system. Secondly, an observer‐based sliding mode controller design problem is investigated for the associated singular Markov jump systems. The highlight of this paper is that we construct an observer‐based mode‐independent integral sliding mode surface function, which is different from the mode‐dependant sliding mode surface function in the previous literatures. Based on this, an observer‐based sliding mode controller is designed to guarantee that the associated singular Markov jump system meets the reachable condition. Finally, a practical example is presented to demonstrate the efficiency and effectiveness of our obtained results.

Dynamic event‐based asynchronous control for T–S fuzzy singular Markov jump systems with redundant channels

This study is concerned with the issue of asynchronous H∞ control for a class of T-S fuzzy singular Markov jump system with redundant channels under a dynamic event-triggered scheme. To save the resource of bandwidth limited network, a dynamic event-triggered scheme is proposed. The technique of redundant channels is adopted to improve the success rate of released data over network, which have been modelled as two mutually independent Bernoulli distributed random variables. The hidden Markov model is utilised to describe asynchronisation phenomena between the system modes and the controller modes. Based on the stochastic Lyapunov functional and the method of free-weighting matrices, the criterion of regular, impulse free and stochastically stable with a certain H∞ performance for the closed-loop system is obtained. The co-design of asynchronous controller and the weighting matrices of the dynamic event-triggered scheme is proposed in terms of a group of feasible linear matrix inequalities. Finally, two examples with dynamic and static event-triggered schemes are given to illustrate the usefulness and effectiveness of the proposed method.

An event-triggered asynchronous H∞ filtering for singular Markov jump systems with redundant channels

In this paper, the problem of asynchronous H∞ filtering for singular Markov jump systems with redundant channels under the event-triggered scheme is studied. In order to save the resource of bandwidth limited network and improve quality of data transmission, we utilize event-triggered scheme and employ redundant channels. The redundant channels are modeled as two mutually independent Bernoulli distributed random variables. To formulate the asynchronization phenomena between the system modes and the filter modes, the hidden Markov model is proposed so that the filtering error system has become a singular hidden Markov jump system. The criterion of regular, causal and stochastically stable with a certain H∞ performance for the filtering error system has been obtained. The co-design of asynchronous filter and the event-triggered scheme is proposed in terms of a group of feasible linear matrix inequalities. Two examples are given to show the effectiveness of the proposed method.

Dissipativity-based asynchronous control for discrete-time singular Markov jump systems with multiplicative noises

The singular systems, which could widely describe more general systems and present traits of physical features, are discussed in this study. Taking the fact that noises always exist in the state and output measurement of one singular system into consideration, which may cause some errors and decrease system performance, this article devotes itself to the dissipative control for discrete-time singular Markov jump systems (SMJSs) with multiplicative noises. To deal with the asynchronous phenomena between the system modes and the controller modes, a set of Markov chains are constructed. To make sure the closed-loop singular system is dissipative, a set of sufficient conditions are derived based on the linear matrix inequalities, and then the asynchronous controller is designed to ensure that SMJSs are stochastically admissible and strictly dissipative. Finally, a simulation example is carried out to verify the correctness of the derived theorem. The designed asynchronous controller improves the robustness of the controller and overcomes the asynchronous phenomenon. This control method can be applied in the fields of robot control system.

Sliding-Mode Control for Singular Markovian Jump Systems With Brownian Motion Based on Stochastic Sliding Mode Surface

In this paper, the stabilization problems for singular Markovian systems with Brownian motion are studied by use of sliding mode control (SMC) with the jumping transfer matrix known, unknown, or partly unknown. At first, a new stochastic sliding mode surface (SSS) is introduced. The problem of state trajectories moving among several sliding mode surfaces can be settled perfectly. By use of the proposed SSS, the sliding mode dynamics of singular Markovian systems with Brownian motion is asymptotically mean square admissible and sufficient design conditions are derived in linear matrix inequalities. Second, by use of a new approach different from the normal Lyapunov method, an SMC law is provided to avoid the state trajectories escaping from the sliding mode surface. Finally, three numerical simulations and one practical simulation are provided to illustrate the validity of the proposed method.

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.

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

The problem of H∞ robust control based on event‐triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event‐triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean‐square admissible and has a prescribed H∞ performance γ. Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method.

Dissipative filtering for singular Markov jump systems with generally uncertain transition rates via new integral inequality approach

This paper considers the problem of dissipative filtering problem for singular Markov jump systems with time-varying delay and generally uncertain transition rates. Firstly, by tuning the improved integral inequality and Wirtinger-based integral inequalities, a sufficient condition is derived to guarantee that the considered system is regular, impulse-free, stochastically stable with the dissipation performance. Then, based on the derived condition, and applying linear matrix inequalities (LMIs) techniques, the filter is synthesized. Finally, some numerical examples are given to illustrate the effectiveness of the obtained theoretic results.

Observer-based control for singular nonhomogeneous Markov jump systems with packet losses

This paper is concerned with the observer-based H∞ control for a class of singular Markov jump systems over a finite-time interval, where the transition probability (TP) is time-varying and is limited to a convex hull. Due to the limited capacity of network medium, packet losses are presented in the underlying systems. Firstly, using a stochastic Lyapunov functional, a sufficient condition on singular stochastic H∞ finite-time boundedness for the corresponding closed-loop error systems is provided. Subsequently, a linear matrix inequality (LMI) condition on the existence of the H∞ observer-based controller is developed from a new perspective. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed controller design method, wherein it is shown that the proposed method yields less conservative results than those in the literature.

Delay-dependent H∞ filtering for discrete singular Markov jump systems with Wiener process and partly unknown transition probabilities

This paper is devoted to the investigation of the delay-dependent H∞ filtering problem for a class of discrete-time singular Markov jump systems with Wiener process and partly unknown transition probabilities. The class of stochastic singular model under consideration is more general and covers the stochastic singular Markov jump time-varying delay systems with completely known and completely unknown transition probabilities as two special cases. Firstly, based on a stochastic Lyapunov–Krasovskii candidate function and an auxiliary vector function, by employing some appropriate free-weighting matrices, the discretized Jensen inequality and combining them with the structural characteristics of the filtering error system, a set of delay-dependent sufficient conditions are established, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, causal and stochastically stable, but also satisfy a prescribed H∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the sufficient conditions for the solvability of the H∞ filtering problem are obtained in terms of a new type of Lyapunov–Krasovskii candidate function and a set of linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed method in the paper.

Delay-dependent H∞ filtering for singular Markov jump systems with Wiener process and generally uncertain transition rates

This paper is devoted to the investigation of the delay-dependent filtering problem for a class of continuous-time singular Markov jump systems with Wiener process and generally uncertain transition rates (GUTRs). In the GUTR stochastic singular model under consideration, based on an auxiliary vector function, by employing an integral inequality and some appropriate free-weighting matrices, the delay-dependent sufficient conditions are derived, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, impulse-free and stochastically stable, but also satisfies a prescribed performance for all time-varying delays no larger than a given upper bound. Furthermore, the solvability conditions of the filtering problem are deduced in terms of a new type of candidate Lyapunov–Krasovskii function and a set of matrix inequalities. Finally, simulation examples are performed to validate the proposed method in this paper.