Singular Stochastic Finite-time Boundedness Research Articles

Observer-based finite-time H∞ control for discrete-time singular Markovian jump systems with asynchronous modes

The asynchronous observer-based finite-time [Formula: see text] control problem for discrete-time singular Markovian jump systems with time-varying delays is studied, where the asynchronism of the controller and observer with respect to the original system is fully taken into consideration. By the use of finite-time analysis theory and the construction of suitable Lyapunov-Krasovskii functionals, sufficient conditions to determine the closed-loop error system is singular stochastic finite-time boundedness are given with [Formula: see text] performance level. Then, by applying linear matrix inequalities, the desired observer parameters and controller parameters can be computed. Finally, the effectiveness of our proposed method is confirmed by simulation.

Event‐based finite‐time H∞ filtering of discrete‐time singular jump network systems

AbstractThis article presents the analysis and design problems of event‐based (EB) finite‐time (FT) filtering for discrete‐time singular Markov jump network systems (SMNSs) based on separation of matrix inequality variables. According to the EB method, an SMNS model of network‐induced delay is introduced. Sufficient conditions of singular stochastic FT boundedness are then obtained for the augmented SMNS model by applying a stochastic Lyapunov functional and introducing slack matrix variables. In addition, using separation schemes for decoupling matrix inequality variables, the EBFT filter gain matrices and triggered ones are co‐designed to ensure that the augmented SMNSs are singularly stochastic FT bounded with a prescribed performance index. Finally, a practical DC test example is presented to show effectiveness of the proposed approach.

Finite-time sliding mode control for networked singular Markovian jump systems with packet losses: A delay-fractioning scheme

The paper is concerned with the finite-time sliding mode control (SMC) problem for a class of discrete networked singular Markovian jump systems (SMJSs) subject to packet losses (PLs) via the delay-fractioning approach. A random variable obeying the Bernoulli distribution is used to depict the phenomenon of PLs, which is frequently encountered in the practical engineering especially during the networked transmission. A key issue to be discussed is how to guarantee both the singular stochastic finite-time boundedness (SSFTB) of the resultant sliding mode dynamic systems and the reachability of the pre-selected sliding surface. Accordingly, a sufficient condition is obtained to ensure the SSFTB of sliding motion based on delay-fractioning method and linear matrix inequality technique. Furthermore, a new SMC mechanism is proposed to compensate the influence induced by LPs and ensure the reachability condition of pre-selected sliding surface simultaneously. Finally, the effectiveness of the proposed SMC approach is tested by a simulation example.

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.

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.

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.

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.

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.

Robust finite-time stabilization of uncertain singular Markovian jump systems

This paper focuses on the problem of robust finite-time stabilization for one family of uncertain singular Markovian jump systems. Firstly, the definitions of singular stochastic finite-time boundedness and singular stochastic H∞ finite-time boundedness are presented. Secondly, sufficient conditions on singular stochastic finite-time boundedness are obtained for the class of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H∞ finite-time boundedness for the family of singular stochastic systems. Sufficient criteria are provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic finite-time boundedness and singular stochastic H∞ finite-time boundedness, which can be reduced to a feasibility problem in the form of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to illustrate the validity of the proposed methodology.

Robust finite-time H∞ control of singular stochastic systems via static output feedback

This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H ∞ finite-time boundedness for the class of singular stochastic systems. Designed algorithm for static output feedback controller is provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic H ∞ finite-time boundedness in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology.