Passivity-based Control for Markovian Jump Systems via Retarded Output Feedback

This paper is concerned with the problem of passivity-based control for Markovian jump systems via retarded output feedback controllers. A delay-dependent passivity criterion is obtained in terms of linear matrix inequalities. Based on this, a sufficient condition is proposed for the design of a retarded output feedback controller which ensures that the closed-loop system is passive. By using the sequential linear programming matrix method, a desired retarded output feedback controller can be constructed. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method.     

Fault-Tolerant Control for Markovian Jump Delay Systems with an Adaptive Observer Approach

This paper investigates the problem of fault estimation and fault-tolerant control for a class of Markovian jump systems with mode-dependent interval time-varying delay and Lipschitz nonlinearities. In this paper, a new adaptive fault observer is designed to solve the problem of fault estimation. The proposed observer can estimate the states and faults simultaneously, whether faults are of time-varying or constant characterization. Based on the fault estimation, a fault-tolerant controller is designed to stabilize the closed-loop system. Sufficient conditions for the existence of the observer gain and fault-tolerant controller gain are got by a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the proposed fault-tolerant control method.     

Robust Fault Detection of Markovian Jump Systems

This paper deals with the problem of observer-based robust fault detection for both continuous- and discrete-time linear Markovian jump systems with an unknown input. By using a fault detection filter as residual generator and a proposed performance index as objective function, the robust fault detection filter design is formulated as an optimization problem. A sufficient condition to solve this problem is established in terms of the feasibility of certain matrix inequalities, which can be solved via iterative linear matrix inequality (LMI) algorithms. The residual evaluation problem is also considered. A numerical example is given to illustrate the effectiveness of the proposed techniques.     

Stability Analysis of Markovian Jump Systems with Multiple Delay Components and Polytopic Uncertainties

This paper investigates the stability problem of Markovian jump systems with multiple delay components and polytopic uncertainties. A new Lyapunov–Krasovskii functional is used for the stability analysis of Markovian jump systems with or without polytopic uncertainties. Two numerical examples are provided to demonstrate the applicability of the proposed approach.     

Mean Square Exponential Stability for Uncertain Delayed Stochastic Neural Networks with Markovian Jump Parameters

This paper is concerned with the problem of delay-dependent mean square exponential stability for a class of delayed stochastic Hopfield neural networks with Markovian jump parameters. The delays here are time-varying delays. Based on a new Lyapunov–Krasovskii functional, delay-dependent stability conditions are derived by means of linear matrix inequalities (LMIs). It is shown that the proposed results can contain some existing stability conditions as a special case. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method, and the simulations show that our results are less conservative than the existing ones.     

Delay-Dependent Robust Stability of Stochastic Uncertain Systems with Time Delay and Markovian Jump Parameters

This paper is concerned with the delay-dependent stability for a class of stochastic uncertain systems with time delay and Markovian jump parameters. The uncertainties considered in this paper are norm-bounded and governed by the Markov process. Un like the topics in the existing literature, the stability criterion is expressed in terms of linear matrix inequalities, which can be efficiently solved by using a convex-optimization algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Passivity Analysis and Passification of Markovian Jump Systems

This paper is concerned with the problems of delay-dependent robust passivity analysis and robust passification for uncertain Markovian jump linear systems (MJLSs) with time-varying delay. The parameter uncertainties are time varying but norm bounded. For the robust passivity problem, the objective is to seek conditions such that the closed-loop system under the state-feedback controller with given gains is passive, irrespective of all admissible parameter uncertainties. For the robust passification problem, desired passification controllers will be designed which guarantee that the closed-loop MJLS is passive. By constructing a proper stochastic Lyapunov–Krasovskii function and employing the free-weighting matrix technique, delay-dependent passivity/passification performance conditions are formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed approaches is demonstrated by a numerical example.     

离散马尔可夫跳变系统的降维观测器设计

针对一类含有未知输入和测量噪声的线性离散时间马尔可夫跳变系统,设计了一种降维观测器,可以对系统中的未知输入和测量噪声同时解耦.以线性矩阵不等式的形式给出观测器存在的充分条件,并确保误差系统有限时间随机稳定;之后利用一种代数重构的思想实现了未知输入的估计;最后通过数值仿真验证了所提方法的有效性.     

Fault Detection for Uncertain Fuzzy Systems Based on the Delta Operator Approach

This paper investigates the problem of designing a robust fault-detection for uncertain T-S fuzzy models based on the delta operator approach. By means of the T-S fuzzy delta operator systems, a fuzzy fault detection filter system is constructed via the delta operator approach. The worst case fault sensitivity has been formulated in terms of linear matrix inequalities. The proposed fault-detection filter not only ensures the H _?-gain from a fault signal to a residual signal greater than a prescribed value, but also guarantees the H _∞-gain from an exogenous input to a residual signal less than a prescribed value in terms of the solvability of linear matrix inequalities. The linear matrix inequalities can be solved by an effective algorithm. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

On Finite-Time Stochastic Stability and Stabilization of Markovian Jump Systems Subject to Partial Information on Transition Probabilities

The problems of finite-time stochastic stability and stabilization for a class of linear Markovian jump systems subject to partial information on transition probabilities are considered in this paper. By introducing the concept of finite-time stochastic stability for linear Markovian jump systems, a new method is proposed to ensure that the state trajectory remains in a bounded region of the state space in mean square sense over a pre-specified finite-time interval. Based on this stability result, the finite-time stochastic stabilization criterion is then given. Finally, two numerical examples are shown to illustrate the effectiveness of the proposed method.     

Delta算子系统的极限环问题分析

Ｄｅｌｔａ算子数字控制器的实现和有限字长研究在高速采样情形下显得尤为重要。本文研究了高速采样时Ｄｅｌｔａ算子系统极限环问题,利用Ｌｙａｐｕｎｏｖ方法给出Ｄｅｌｔａ系统极限环的判别条件,并给出具体实现例子证明了结论的有效性。     

Robust H ∞ Control for Stochastic Time-Delay Systems with Markovian Jump Parameters via Parameter-Dependent Lyapunov Functionals

This paper deals with the problems of robust stabilization and robust H _∞ control for time-delay stochastic systems with Markovian jump parameters and convex polytopic uncertainties. The purpose is the design of state feedback controllers such that the closed-loop system is robustly exponentially stable in the mean square and satisfies a prescribed H _∞ performance level. Sufficient conditions for the solvability of the problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that desired state feedback controllers can be designed by solving a set of linear matrix inequalities.     

Admissible Control of Linear Singular Delta Operator Systems

In this paper, we study the problem of state feedback admissible control for the linear singular delta operator systems that result from linear singular continuous systems. By introducing the concept of delta operator, for a given linear singular continuous system, we establish its corresponding delta operator model and this discrete model converges to its continuous counterpart as the sampling period decreases. Sufficient conditions for desirable controllers in terms of matrix inequalities and linear matrix inequalities are given, and the explicit expressions of the controllers are derived. Some examples as well as numerical simulations are provided to demonstrate the effectiveness of the proposed approaches.     

Robust Adaptive Sliding Mode Control for Nonlinear Uncertain Neutral Markovian Jump Systems

This paper investigates the robust adaptive sliding mode control problem for a class of nonlinear uncertain neutral Markovian jump systems. In this study, the system state is unmeasurable and the upper norm bounds of the nonlinear functions are unavailable. An observer-based adaptive sliding mode controller is synthesized to render the resulting error system stochastically stable with a prescribed disturbance attenuation level. Finally, a numerical example is exploited to demonstrate the effectiveness of the control scheme.     

Dynamic Anti-Windup Control Design for Markovian Jump Delayed Systems with Input Saturation

This paper deals with the problem of robust stabilization for Markovian jump delayed systems with partially known transition rates subject to input saturation. The problem we address is the design of dynamic anti-windup compensators, which guarantee that the resulting closed-loop constrained systems are robustly mean-square stable. By employing local sector conditions and an appropriate Lyapunov-Krasovskii function, some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method.     

Robust Fault Detection of Uncertain Time-Delay Markovian Jump Systems with Different System Modes

In this paper, a robust fault detection filter (RFDF)design scheme is presented for uncertain nonlinear Markovian jump systems with mixed delays. By using a observer-based fault detection filter as residual generator, the RFDF design is formulated as an H _∞-filtering problem. Particularly, two different Markov processes are considered for modeling the randomness of system matrix and the state delay; meanwhile, the corresponding two kinds of transition rate matrices are assumed to be incompletely accessible, that is, the one with partially unknown entries and the other with polytopic uncertainties. By using a new convex polyhedron technique, some new sufficient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) to synthesize the residual generation scheme. Finally, a numerical example is given to illustrate the effectiveness of the proposed techniques.     

Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities

This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discretevalued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.     

Stochastic Stabilization of Markovian Jump Systems with Partial Unknown Transition Probabilities and Actuator Saturation

The stochastic stabilization problem of Markovian jump systems subject to both partial unknown transition probabilities and actuator saturation is considered in this paper. Different from the previous results where complete knowledge on the transition probabilities is available, a new controller synthesis scheme is proposed as well as an estimate of the domain of attraction in mean square sense. A sufficient condition is first 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, a numerical example is provided to show the effectiveness of our method.     

Delay-Dependent Passivity and Passification for Uncertain Singularly Perturbed Markovian Jump Systems with Time-Varying Delay

This paper is concerned with passivity analysis and passivity-based controller design for uncertain singularly perturbed Markovian jump systems with time-varying delay in an interval. Firstly, a delay-dependent condition for the considered system to be mean-square exponentially stable and robustly passive is derived in terms of linear matrix inequality. Then, the passification problem is investigated. Based on the obtained passivity condition, the existence of the desired state feedback controller is established. Numerical examples are presented to show the effectiveness of the proposed method.