Almost sure stability of second‐order nonlinear stochastic system with Lévy noise via sliding mode control

Xia

Shen

et al. 2020

This paper investigates pth moment regional stability, stabilization, and generalized pole assignment of stochastic systems, which are most useful in many specific systems and applications. With the help of the generalized -representation method, the necessary and sufficient conditions of pth moment regional stability and stabilization of stochastic systems are addressed.Meanwhile, the generalized pole assignment of stochastic systems is also considered. Finally, two examples are presented to show the effectiveness of the proposed methods. K E Y W O R D Spth moment -stability, generalized -representation, generalized pole assignment, power vector 1 3234 /journal/rnc Int J Robust Nonlinear Control. 2020;30:3234-3249.ZHANG et al. 3235control system. Frequently used pole assignment regions are generally including negative semi-plane, sector, disk, vertical stripe, and the intersection of them. Regional pole assignment of the linear deterministic system has been investigated in various aspects, such as robustness bounds of pole clustering, 12 robust pole placement, 13,14 and H 2 or H ∞ performance with pole placement constraints. 15,16 Recently, the -representation has been explicitly presented in Reference 17. As the most advantage of this method, many classical results of linear systems could be directly applied to the stochastic systems. [17][18][19][20][21][22] For example, Reference 17 proposed the concept of -representation method, and discussed the problem of generalized -stability/stabilization for linear stochastic systems. The stabilization with state-multiplicative noise was investigated, and the infinite horizon stochastic H 2 ∕H ∞ control with state-dependent and control-dependent noise were studied in Reference 20. Moment stability theorems for the systems with the stability properties were considered in Reference 22. However, it should be pointed out that the -representation method will be no longer valid for the corresponding cases in the meaning of pth moment stability/stabilization although it effectively solves the mean square stability and other related issues for the stochastic linear systems.Motivated by the pole placement, the -representation method and Itô formula, we will generalize the state matrix of the linear stochastic system to the extended state matrix by using the generalized -representation technique. The quadratic terms of the state vector in -representation could be extend to pth terms using the lexicographical order of the monomials. Then, the problems of pth moment regional stability, stabilization, and the generalized pole assignment of linear stochastic systems could be handled effectively as the means of the deterministic system. The main advantages of the proposed approach can be summarized as follows.First, the linear stochastic systems can be transformed into deterministic systems with the state matrixÂ n⋅p and the state vector x {p} by the generalized -representation method, which is the generalization of -representation in Reference 17. Then, the problems of p...

Section: Corollary 2 the Linear Stochastic Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pth moment regional stability/stabilization and generalized pole assignment of linear stochastic systems: Based on the generalized ‐representation method

Xia

Shen

et al. 2020

“…In References 17 and 18, asynchronous control methods were proposed for Markovian jump systems. In References 19‐25 some other methods are proposed for the control problem of stochastic systems. Observers are designed for fault detection in stochastic systems in References 26‐28.…”

Section: Introductionmentioning

confidence: 99%

Incipient fault prediction for nonlinear stochastic distribution systems

Yao

2022

In order to avoid the occurrence of major accidents in the industrial production process, incipient fault prediction that can predict fault in advance has attracted more and more attentions. In this article, a generalized correntropy filtering‐based incipient fault prediction strategy is proposed, which is suitable for nonlinear stochastic distribution systems with simultaneous actuator and sensor faults and non‐Gaussian noise. Three filters are designed to predict the incipient fault of nonlinear stochastic distribution systems: the first one is used to predict the time when the incipient fault occurs, and the other two are used to estimate the evolution rate of sensor fault and actuator fault, respectively. When the residual signal exceeds the predetermined threshold, the fault is detected and the time of occurrence can be also estimated. Once the fault is detected, the designed filter can be used to estimate the evolution rate of the unknown fault. After estimating the time of fault appearance and its evolution rate, the change process of incipient fault can be predicted. Finally, an example of a chemical reaction process is given to illustrate the validity of the prediction scheme.

“…Due to their extensive application, a great amount of concern has been paid to time‐delay systems. Recently, the study of time‐delay systems has been very active, and has been deeply involved in various branches, such as stability analysis, 1‐5 robust control, 6‐10 H ∞ control, 11‐14 and passive/dissipative control 15‐18 …”

Section: Introductionmentioning

confidence: 99%

Interval stability and interval stabilization of linear stochastic systems with time‐varying delay

Xia

Park

et al. 2021

This article first investigates the criterion of interval stability for linear stochastic systems with time‐varying delay via equivalent systems and Lyapunov–Krasovskii (L‐K) functionals. Different from existing stability conditions, the criterion of interval stability can be used to make a more accurate judgment of the stability for linear time‐delay systems. In other words, the new criterion can judge not only the stability of the system but also the speed of its convergence. Meanwhile, based on the criterion of the interval stability, the condition of interval stabilization is derived, which cannot only ensure the stability of the linear time‐delay systems, but also adjust the convergence rate of the states to the ideal level. A numerical instance is presented to illustrate the advantages of the resulting interval stabilization criterion.