Uncertain Stochastic Time-delay Systems Research Articles

Non-fragile [formula omitted] finite-time sliding mode control for stochastic Markovian jump systems with time delay

This article mainly discusses the realization of H∞ finite-time control for a class of uncertain stochastic time-delay systems with unmeasured states through sliding mode control (SMC). The purpose of this paper is to design a suitable SMC controller to suppress the influence of factors such as model switching and time delay on the system performance, so that the system state can be stabilized within a limited time interval. First, the state of the system is reconstructed through the H∞ state observer, and the SMC law based on the state observer is designed so that the state trajectory reaches the specified sliding surface (s.s.s) in a given finite time. Next, by introducing the concept of time-partitioning strategy, the finite-time boundedness (FTBs) of the reaching phase and the sliding motion phase are realized respectively. Then, according to the linear matrix inequality(LMI), the asymptotic stochastic stability of the system and sufficient conditions for sliding mode dynamics with a given interference attenuation level are derived. Finally, the numerical example and single-link robot arm model (S-lram) show the effectiveness of the method.

Non‐fragile robust exponential stabilisation and control for uncertain stochastic systems with non‐linearity and mixed delays

This study focuses on the delay-dependent robust exponential stabilisation and H ∞ control for uncertain stochastic time-delay systems with non-linear terms. Uncertain parameters are assumed to be time-varying norm bounded, while time-varying delay terms include both discrete and distributed delays. Firstly, by choosing an appropriate Lyapunov–Krasovskii functional, a sufficient condition for the robust exponential stabilisation is obtained. Secondly, the H ∞ control is also discussed. All criteria are presented in the form of linear matrix inequalities with less conservatism. Finally, an example verifies the validity of the proposed method.

New delay-dependent observer-based control for uncertain stochastic time-delay systems

This paper considers the problem of estimating the state vector of uncertain stochastic time-delay systems, while the system states are unmeasured. The system under study involves parameter uncertainties, noise disturbances and time delay, and they are dependent on the state. Based on the Lyapunov–Krasovskii functional approach, we present a delay-dependent condition for the existence of a state observer in terms of a linear matrix inequality. A numerical example is exploited to show the validity of the results obtained.

Composite Robust <inline-formula> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> Control for Uncertain Stochastic Nonlinear Systems With State Delay via a Disturbance Observer

In this note, the robust stochastic stabilization and robust $H_\infty$ control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, a composite hierarchical control scheme is proposed that integrates the output of the disturbance observer with the state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite hierarchical controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation. It has been shown that the disturbance rejection performance can also be achieved. A numerical example is provided to show the potential of the proposed techniques and encouraging results have been obtained.

Integral sliding mode control for robust stabilisation of uncertain stochastic time-delay systems driven by fractional Brownian motion

ABSTRACTIn this paper, the stability and controller design for fractional stochastic systems, i.e. stochastic systems driven by fractional Brownian motion (fBm) are investigated. A fractional infinitesimal operator is proposed for stability analysis of this class of stochastic systems and a Lyapunov-based stability criterion is established. Thereafter, the presented stability criterion is utilised to develop the sliding mode control scheme for fractional stochastic systems with state delay and time-varying uncertainties. By applying the proposed fractional infinitesimal operator, the sufficient robust stability conditions are derived in the form of linear matrix inequalities. The proposed method guarantees the reachability of the sliding surface in finite time, and the closed-loop system will be stable in probability for all Hurst indices of the fBm in the range . Finally, some simulation examples are given to illustrate the effectiveness of the proposed design method.

Robust stabilization andH∞control of uncertain stochastic time-delay systems with nonlinear perturbation

Summary This paper investigates the problem of delay-dependent robust stochastic stabilization and H∞ control for uncertain stochastic nonlinear systems with time-varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H∞ control for uncertain stochastic system with time-varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed-loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.

New Stability Criteria for Uncertain Nonlinear Stochastic Time-Delay Systems

This paper deals with the problem of robust stabilization and non-fragile robust control for a class of uncertain stochastic nonlinear time-delay systems that satisfy a one-sided Lipschitz condition. The parametric uncertainties are assumed to be real time-varying and norm bounded. Based on the one-sided Lipschitz condition including useful information of the nonlinear part, a new stability criterion for this class of nonlinear systems is provided. A memoryless non-fragile state-feedback controller is designed to guarantee robust stochastic stability of closed-loop systems. The approach of linear matrix inequalities is proposed to solve the robust stability for stochastic nonlinear systems with time-varying delay, and to obtain new delay-dependent sufficient conditions. Numerical examples are given to illustrate the validity and advantages of the proposed theoretical results.

Fuzzy fault-detection filtering for uncertain stochastic time-delay systems with randomly missing data

This paper is concerned with the robust H∞ fault-detection problem for a class of uncertain discrete stochastic Takagi–Sugeno fuzzy systems with time-varying delays, parameter uncertainties and randomly missing data in a network environment. We deal with the fault detection by designing fuzzy-rule-independent and fuzzy-rule-dependent fault detection filters, which guarantee the fault detection system is not only robustly stochastically stable, but also satisfies a prescribed H∞ performance level for all admissible uncertainties. Lyapunov stability theory and the linear matrix inequality technique are utilized to derive novel conditions for the desired fault detection filters. The residual evaluation function and detection threshold are also discussed in order to detect the occurrence of faults. A numerical example and a nonlinear mass-spring-damper mechanical system are provided to demonstrate that our fault-detection system is sensitive to faults and simultaneously robust to disturbances.

Non‐fragile robust stabilization and H ∞ control for uncertain stochastic time delay systems with Markovian jump parameters and nonlinear disturbances

SUMMARYThis paper considers the problems of non‐fragile robust stabilization and H ∞ control for uncertain stochastic time delay systems with Markovian jump parameters and nonlinear disturbances. The parameter uncertainties are assumed to be time‐varying norm bounded appearing in both state and input matrices. The purpose of the non‐fragile robust stabilization problem is to design a memoryless non‐fragile state feedback controller such that the closed‐loop system is robustly stochastically stable for all admissible uncertainties in both the system and controller. In addition to the aforementioned requirement, a prescribed H ∞ performance level is required to be achieved for the non‐fragile robust H ∞ control problem. With the use of the Lyapunov–Krasovskii functional method and free‐weighting matrices, delay‐dependent sufficient conditions for the solvability of these problems are obtained in terms of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

Passive Control for Uncertain Stochastic Time-Delay Systems

This paper investigates the problems of delay-dependent passive analysis and control for uncertain stochastic systems with time-varying delay and norm-bounded parameters uncertainties. Delay-dependent stochastic passive condition for the uncertain stochastic time-delay systems is obtained based on Laypunov-Krasovkii functional approach. On the basis of this condition, a delay-dependent passive controller is presented. Sufficient condition for the existence of desired controller is formulated in terms of linear matrix inequality. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Robust H ∞ Filtering for Uncertain Nonlinear Stochastic Systems with Mode-dependent Time-delays and Markovian Jump Parameters

This paper investigates the problem of robust H ∞ filtering for a class of uncertain nonlinear stochastic time-delay systems with Markovian jump parameters. The system under consideration contains parameter uncertainties, Ito-type stochastic disturbances, unknown nonlinearities as well as time-varying delays, which vary in a range and dependent on the mode of the operation. We aim to design a full-order Markovian jump filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable in the mean square, and a prescribed H ∞ disturbance attenuation level is guaranteed. By using the Lyapunov stability theory and Ito differential rule, some sufficient conditions in terms of linear matrix inequality (LMI) are proposed to guarantee the existence of the desired H ∞ filter. Then, the explicit expressions of the desired filter parameters are given. Illustrative examples are provided to demonstrate the effectiveness and applicability of the proposed method.

Improved L 2–L ∞ filtering for stochastic time-delay systems

The L2–L∞ filtering problem for continuous-time polytopic uncertain stochastic time-delay systems is investigated. The main purpose is to design a full-order filter guaranteeing a prescribed L2–L∞ attenuation level for the filtering error system. A simple alternative proof is given for an enhanced LMI (linear matrix inequality) representation of L2–L∞ performance. Based on the criterion which keeps Lyapunov matrices out of the products of system dynamic matrices, a sufficient condition for the existence of a robust estimator is formulated in terms of LMIs. The corresponding filter design is cast into a convex optimization problem. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.

Robust H [formula omitted] exponential filtering for uncertain stochastic time-delay systems with Markovian switching and nonlinearities

In this paper, we deal with the robust H ∞ exponential filtering problem for a class of uncertain stochastic time-delay systems with Markovian switching and nonlinear disturbances. The system under consideration involves parameter uncertainties, It o ˆ -type stochastic disturbances, Markovian jump parameters, unknown nonlinear disturbances as well as time-varying delays, which vary in a range and dependent on the mode of the operation. The aim of this problem is to design a Markovian jump exponential filter such that the filtering error system is robustly stochastically exponentially mean-square stable, and a prescribed H ∞ disturbance attenuation level is guaranteed. Novel delay-range-dependent sufficient conditions are proposed to guarantee the existence of the desired robust exponential filter, which are derived in terms of linear matrix inequalities (LMIs). Then, the explicit expression of the desired filter parameters is characterized. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method.

Robust observer design for uncertain Itô neutral stochastic time-delay systems via sliding mode control

This paper deals with the output feedback sliding mode control for uncertain Ito neutral stochastic time-delay systems. The system states are unmeasured, and the uncertainties are unmatched. A sliding mode control scheme is proposed based on the state estimates. By utilizing a novel switching function, the derivative of the switching function is ensured to have a finite variation. It is shown that the sliding mode in the estimation space can be attained in finite time. A sufficient condition for the asymptotic stability (in probability) of the overall closed-loop stochastic system is derived. Finally, a simulation example is given to illustrate the proposed method.

Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems

This paper deals with the problem of non-fragile guaranteed cost control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are assumed to be time-varying and norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square for all admissible parameter uncertainties and the closed-loop cost function value is not more than a specified upper bound. A new sufficient condition for the existence of such controllers is presented based on the linear matrix inequality (LMI) approach. Then, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function. Numerical example is given to illustrate the effectiveness of the developed techniques.

Robust reliable H-infinity control for nonlinear uncertain stochastic time-delay systems with Markovian jumping parameters

This paper deals with the problems of robust reliable exponential stabilization and robust stochastic stabilization with H-infinity performance for a class of nonlinear uncertain time-delay stochastic systems with Markovian jumping parameters. The time delays are assumed to be dependent on the system modes. Delay-dependent conditions for the solvability of these problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that the desired state feedback controller can be designed by solving a set of linear matrix inequalities. Finally, the simulation is provided to demonstrate the effectiveness of the proposed methods.

Formula omitted] filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities

In this paper, we deal with the robust H ∞ filtering problem for a class of uncertain nonlinear time-delay stochastic systems. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, time-varying delays, as well as sector-bounded nonlinearities. We aim at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed H ∞ disturbance rejection attenuation level. By using the Lyapunov stability theory and Itô’s differential rule, sufficient conditions are first established to ensure the existence of the desired filters, which are expressed in the form of a linear matrix inequality (LMI). Then, the explicit expression of the desired filter gains is also characterized. Finally, a numerical example is exploited to show the usefulness of the results derived.

Delay-Dependent Robust H∞ Control of Uncertain Stochastic Delayed Systems

This paper is concerned with robust H∞ control for uncertain stochastic time-delay systems with norm-bounded parametric uncertainties. Based on an integral inequality and slack matrix technique, delay-dependent bounded real lemma (BRL) and the condition for the existence of robust H∞ controller are presented. For all the admissible parametric uncertainties, the designed controller guarantees the resulting closed-loop system is robustly mean-square asymptotically stable with a prescribed H∞ disturbance attenuation level. The results are formulated in terms of linear matrix inequalities (LMIs). Both model transformation and cross terms bounding techniques are avoided in the derivations. Two numerical examples are provided to show the advantage of the proposed method.

Delay-range-dependent robust H ∞ filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters

This paper investigates the problem of robust H ∞ filtering for uncertain stochastic time-delay systems with Markovian jump parameters. Both the state dynamics and measurement of the system are corrupted by Wiener processes. The time delay varies in an interval and depends on the mode of operation. A Markovian jump linear filter is designed to guarantee robust exponential mean-square stability and a prescribed disturbance attenuation level of the resulting filter error system. A novel approach is employed in showing the robust exponential mean-square stability. The exponential decay rate can be directly estimated using matrices of the Lyapunov–Krasovskii functional and its derivative. A delay-range-dependent condition in the form of LMIs is derived for the solvability of this H ∞ filtering problem, and the desired filter can be constructed with solutions of the LMIs. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.

Robust L2 - L∞ Filtering for Uncertain Nonlinearly Parameterized Stochastic Systems with Time-Varying Delays

This paper is concerned with the problem of robust L2 - L∞ filtering for uncertain stochastic time-delay systems in the nonlinear fractional transformation (NFT) form. Attention is focused on the design of both full-order and reduced-order filters, guaranteeing robust stochastic stability and a prescribed level of L2 - L∞ performance for the filtering error system. A parameter-dependent Lyapunov functional is employed to solve the problem. The concerned filters are not only parameter dependent but also have the NFT form. Sufficient conditions for the existence of such filters are presented in terms of certain linear matrix inequalities (LMIs). Desired filters are explicitly expressed based on the solutions to the proposed LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.