Stochastic Finite-time Boundedness Research Articles

Robust observer-based finite-time [formula omitted] control for discrete-time singular Markovian jumping system with time delay and actuator saturation

This paper is concerned with the problem of robust observer-based finite-time H∞ control for discrete-time singular Markovian jumping system with time-varying delay and actuator saturation. By using linear matrix inequality (LMI) approach and constructing proper Lyapunov–Krasovskii functional, sufficient criteria have been obtained that ensure the system singular stochastic finite-time boundedness and singular stochastic finite-time H∞ boundedness. Then the observer and feedback controllers are designed, and with the following the results are extended to convex optimization problems so that the optimal values of attenuation level and the maximum saturation attraction domain can be calculated directly. In the end, some numerical examples are presented to show the feasibility and validity of the proposed results.

Asynchronous output feedback control of time-varying Markovian jump systems within a finite-time interval

This work addresses the asynchronous output feedback control for time-varying Markovian jump systems. The parameter uncertainties enter the system in random ways according to a determined mode-dependent Bernoulli distributed white sequence. The non-synchronization phenomenon between the system modes and controller modes is modeled as a hidden Markov model. By means of intensive stochastic analysis and recursive matrix inequality techniques, sufficient conditions are attained to ensure the finite-time stochastic boundedness of the closed-loop system with a satisfied H∞ disturbance rejection level. Moreover, an iterative algorithm is established for designing asynchronous output feedback controller. Finally, simulation results are given to illustrate the proposed design scheme.

Event-Based Finite-Time Filtering for Multirate Systems With Fading Measurements

In this paper, the finite-time filtering problem is investigated for a class of wireless networked multirate systems (NMSs) with fading channels. The system measurements are transmitted through fading channels described by a modified stochastic Rice fading model, and the event-based wireless relay communication scheme is proposed to determine whether the received fading measurements in the relay nodes should be transmitted to the filter. With the aid of the stochastic analysis approach, sufficient conditions are established under which the stochastic finite-time boundedness (FTB) of the estimation error dynamics is guaranteed and the prescribed finite-time $H_{\infty }$ performance constraint is achieved. Based on the derived conditions, the addressed finite-time filtering problem of NMSs is recast as a convex optimization one that can be solved via the semidefinite program method. Furthermore, the explicit expression of the desired filter is obtained by means of the feasibility of certain matrix inequalities. Two additional optimization problems are considered with respect to the FTB parameter and the finite-time $H_{\infty }$ performance index. Finally, a numerical simulation example on a continuous stirred tank reactor is employed to show the effectiveness of the filtering scheme proposed in this paper.

Reliable finite-time H∞ control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay

ABSTRACTThis paper investigates the problem of reliable finite-time H∞ control for one class of uncertainsingular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. Continuous fault model is more general and practical to serve as the actuator fault. Time delay is a kind of positive time-varying differentiable bounded delays. First, based on a state estimator the resulting closed-loop error system is constructed and sufficient criteria are provided to guarantee that the augmented system is singular stochastic finite-time boundedness and singular stochastic H∞ finite-time boundedness in both normal and fault cases via constructing a delay-dependent Lyapunov–Krasonskii function. Then, the gain matrices of state-feedback controller and state estimator are fixed by solving a feasibility problem in terms of linear matrix inequalities through decoupling technique, respectively. Finally, numerical examples are given to show the validity of the proposed design approach.

Resilient and robust finite-time H∞ control for uncertain discrete-time jump nonlinear systems

• Investigating the resilient and robust finite-time H ∞ control for DMJNSs. • Designing a controller to ensure that DMJNSs are SFTS, SFTB or SH ∞ FTB for DMJNSs. • Presentation of LMI-based conditions to deal with the feasibility issues. • The effectiveness of proposed approaches is illustrated by numerical examples. This paper studies the robust and resilient finite-time H ∞ control problem for uncertain discrete-time nonlinear systems with Markovian jump parameters. With the help of linear matrix inequalities and stochastic analysis techniques, the criteria concerning stochastic finite-time boundedness and stochastic H ∞ finite-time boundedness are initially established for the nonlinear stochastic model. We then turn to stochastic finite-time controller analysis and design to guarantee that the stochastic model is stochastically H ∞ finite-time bounded by employing matrix decomposition method. Applying resilient control schemes, the resilient and robust finite-time controllers are further designed to ensure stochastic H ∞ finite-time boundedness of the derived stochastic nonlinear systems. Moreover, the results concerning stochastic finite-time stability and stochastic finite-time boundedness are addressed. All derived criteria are expressed in terms of linear matrix inequalities, which can be solved by utilizing the available convex optimal method. Finally, the validity of obtained methods is illustrated by numerical examples.

Finite-Time Distributed State Estimation Over Sensor Networks With Round-Robin Protocol and Fading Channels.

This paper considers finite-time distributed state estimation for discrete-time nonlinear systems over sensor networks. The Round-Robin protocol is introduced to overcome the channel capacity constraint among sensor nodes, and the multiplicative noise is employed to model the channel fading. In order to improve the performance of the estimator under the situation, where the transmission resources are limited, fading channels with different stochastic properties are used in each round by allocating the resources. Sufficient conditions of the average stochastic finite-time boundedness and the average stochastic finite-time stability for the estimation error system are derived on the basis of the periodic system analysis method and Lyapunov approach, respectively. According to the linear matrix inequality approach, the estimator gains are designed. Finally, the effectiveness of the developed results are illustrated by a numerical example.

Event-based finite-time state estimation for Markovian jump systems with quantizations and randomly occurring nonlinear perturbations

This paper is concerned with finite-time state estimation for Markovian jump systems with quantizations and randomly occurring nonlinearities under event-triggered scheme. The event triggered scheme and the quantization effects are used to reduce the data transmission and ease the network bandwidth burden. The randomly occurring nonlinearities are taken into account, which are governed by a Bernoulli distributed stochastic sequence. Based on stochastic analysis and linear matrix inequality techniques, sufficient conditions of stochastic finite-time boundedness and stochastic H∞ finite-time boundedness are firstly derived for the existence of the desired estimator. Then, the explicit expression of the gain of the desired estimator are developed in terms of a set of linear matrix inequalities. Finally, a numerical example is employed to demonstrate the usefulness of the theoretical results.

Finite-time [formula omitted] fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions

This paper addresses a finite-time H∞ fuzzy control problem for a class of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions, which is represented as a Takagi–Sugeno (T–S) fuzzy model. A new homogeneous polynomial of partly uncertain transition rates is chosen. Free-matrix-based and double integral forms of the Wirtinger-based integral inequalities are employed to make the proposed approach less conservative. Then sufficient conditions are derived such that the fuzzy nonlinear Makovian jump delayed system exhibits stochastic finite-time boundedness. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methodology.

Robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation

In this paper, the problem of robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation is studied. First, sufficient conditions that guarantee the systems singular stochastic finite-time boundedness are derived via constructing a delay-dependent Lyapunov–Krasonskii functional and linear matrix inequalities (LMI) approaches. Then the results are extended to singular stochastic finite-time H∞ boundedness. Furthermore, with these conditions and convex optimization arithmetic, the design method of H∞ controller and conditions that ensure the H∞ disturbance attenuation level are obtained. Finally, some numerical examples are presented to illustrate the validity and efficiency of the proposed methods.

Robust and non-fragile finite-time H∞ control for uncertain Markovian jump nonlinear systems

This paper investigates the non-fragile and robust finite-time H∞ control problem for a class of uncertain Markovian jump nonlinear systems with bounded parametric uncertainties and norm-bounded disturbance. By employing stochastic analysis and linear matrix inequality techniques, sufficient criteria of stochastic finite-time boundedness and stochastic H∞ finite-time boundedness are first provided for the class of stochastic jump systems. Then, a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite-time bounded and have an H∞ attention performance level by utilizing matrix decomposition approach. Furthermore, the analysis and design of non-fragile and robust finite-time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite-time boundeded with a prescribed attention index by using non-fragile control technique. In addition, we also deal with the analysis and design of stochastic finite-time stability and stochastic finite-time stabilization. All criterions can be characterized in terms of linear matrix inequalities. Finally, two examples are also given to illustrate the effectiveness of obtained results.

Finite-time filtering for T–S fuzzy jump neural networks with sector-bounded activation functions

This paper is concerned with the problems of finite-time filter analysis and design for discrete time-delay neural networks with Markovian jump parameters and sector-bounded activation functions represented by Takagi–Sugeno fuzzy model. Firstly, a sufficient admissibility criterion is presented to guarantee that the augmented fuzzy jump neural network without parameter uncertainties is stochastically finite-time bounded in a prescribed time interval. From the admissibility criterion obtained, a sufficient condition on stochastic finite-time boundedness is provided for the augmented fuzzy jump neural networks. Then, a sufficient criterion to design a finite-time fuzzy filter is presented with uncertain parameters and Markovian jumps for discrete time-delay fuzzy neural networks. Moreover, conditions on stochastic finite-time stability are also established for nominal and uncertain delayed fuzzy jump neural networks without the presence of external disturbance. All criteria obtained can be represented as the form of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.

Stochastic finite-time boundedness on switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities

In this paper, problems of finite-time boundedness are investigated for a class of discrete-time switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities. The time-varying transition probabilities are described by a piecewise-constant matrix subject to a high-level average dwell time (ADT) switching. Sensor and actuator saturations are characterized by a vector-valued decomposition method and the stochastic nonlinearities are approximated by a statistical method. In general, not all trajectories originating from the admissible initial states could be stabilized in the mean square sense or sufficient conditions are too restrictive to yield feasible solutions. Therefore, the purpose of studying the problems addressed here is to design an output feedback controller via the ADT approach such that the resulting closed-loop systems are stochastically finite-time bounded and have a guaranteed disturbance attenuation capability. Simulation results demonstrate the potential and effectiveness of the theoretical results.

Finite-time [formula omitted] static output control of Markov jump systems with an auxiliary approach

This paper considers the finite-time H∞ static output feedback control of Markov jump systems. With the help of introducing two new variables related to the original system state and output, sufficient conditions for the closed-loop system to be stochastic finite-time boundedness with the prescribed H∞ performance level are proposed in terms of linear matrix inequalities (LMIs). Meanwhile, the static output control gains are solved explicitly by the proposed conditions. It is shown that the proposed method is less or at least the same conservative than the existing result. Lastly, a numerical example is given to demonstrate the effectiveness of the proposed method.

Finite-time stochastic boundedness of discrete-time Markovian jump neural networks with boundary transition probabilities and randomly varying nonlinearities

This work studies the problem of finite-time stochastic boundedness of discrete-time Markovian jump neural networks with boundary transition probabilities and randomly varying nonlinearities. The partly unknown and uncertain transition probabilities (TPs) are included in the paper, and more general nonlinearities are introduced with both upper and lower bounds due to the nature of its probability information. By employing the free-weighting matrix technique, finite-time stability theory and boundary incomplete TPs, the solvability sufficient conditions of finite-time stochastic boundedness are given. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approach.

Finite-time fault tolerant control of uncertain singular Markovian jump systems with bounded transition probabilities

This paper is concerned with the problem of finite-time fault-tolerant control for one family of uncertain singular Markovian jump with bounded transition probabilities and nonlinearities systems. The actuator faults are presented as a more general and practical continuous fault model. Partially known transition rate parameters have given lower and upper bounds. Firstly, the resulting closed-loop error system is constructed based on a state estimator; sufficient criteria are provided to guarantee that the augmented system has singular stochastic finite-time boundedness and singular stochastic $$H_\infty $$ finite-time boundedness in both normal and fault cases. Then, by employing a decoupling technique, the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to demonstrate the effectiveness of the proposed design approach.

Reliable finite-time H∞ filtering for discrete time-delay systems with Markovian jump and randomly occurring nonlinearities

This paper is concerned with the problem of reliable finite-time H∞ filtering for discrete time-varying delay systems with Markovian jump and randomly occurring nonlinearities (RONs). RONs are introduced to model a class of sector-like nonlinearities that occur in a probabilistic way according to a two-dimensional discrete random variables joint distribution. The failures of sensors are quantified by a variable varying in a given interval. The time-varying delay is unknown with given lower and upper bounds. Firstly, the filtering errr dynamic system is constructed based on an H∞ filter, sufficient criteria are provided to guarantee that the resulting filtering error system is stochastic finite-time boundedness and stochastic finite-time H∞ filtering in both normal and fault cases. The gain matrices of the controller and filter are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to demonstrate the effectiveness of the proposed design approach.

Finite-time [formula omitted] control for singular Markovian jump systems with partly unknown transition rates

This paper investigates the problem of finite-time H∞ control for a class of singular Markovian jump systems with partly unknown transition rates. Firstly, sufficient conditions on singular stochastic finite-time boundedness of singular Markovian jump systems with partly unknown transition rates are obtained. Secondly, the results are extended to singular stochastic H∞ finite-time boundedness of singular Markovian jump systems with partly unknown transition rates. Then state feedback controllers are designed to ensure the singular stochastic finite-time boundedness and the singular stochastic H∞ finite-time boundedness of the underlying closed singular Markovian jump systems in the forms of strict LMIs. Finally, numerical examples are given to illustrate the validity of the proposed methods.

Finite-TimeH∞Filtering for Singular Stochastic Markovian Jump Systems with Time-Varying Delays

The issue of finite-timeH∞filtering for singular stochastic Markovian jump systems with time-varying delays is concerned in this paper.H∞filtering is designed for underlying closed-loop singular Markovian jump system and system state does not exceed a given bound over some finite-time interval. Considering the full information of underlying Markov process, sufficient conditions are obtained to guarantee that the described system is finite-time stability andH∞filtering finite-time boundedness. By establishing the results of stochastic character and finite-time boundedness, the closed-loop singular Markovian jump system trajectory stays within the given bound. At last, a numerical example is supplied to show the efficiency of the proposed method.

Finite‐time analysis and design for discrete‐time switching dynamics Markovian jump linear systems with time‐varying delay

The problems of finite-time analysis and design for a class of discrete-time switching dynamics Markovian jump linear systems (SD-MJLSs) with time-varying delay are investigated in this study. The considered systems could be viewed as Markovian jump linear systems governed by a piecewise-constant transition probability matrix, which is subject to a high-level average dwell time (ADT) switching. The time delay is considered as time varying and has a lower and upper bound. First, sufficient conditions, which guarantee the stochastic finite-time boundedness of the underlying systems, are presented by employing the ADT approach. These conditions are not only dependent on the delay upper bound but also the delay range. Then, a finite-time weighted l 2 gain of such delay SD-MJLSs is obtained to measure the disturbance attenuation capability over a fixed time interval and the design of the stabilising controller is further given. Moreover, an improved controller design method, which could provide efficiency and practicability, is further developed. Finally, a numerical example is given to verify the potential of the developed results.

Stochastic finite-time boundedness for Markovian jumping neural networks with time-varying delays

In this paper, a novel method is developed for the finite-time boundedness of Markovian jumping neural networks with time-varying delays. By introducing a newly augmented stochastic Lyapunov–Krasovskii functional and novel activation function conditions, sufficient condition for Markovian jumping neural networks is presented, and the state trajectory remains in a bounded region over a pre-specified finite-time interval. Finally, numerical examples are given to illustrate the efficiency and less conservative of the proposed method.