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This paper studies the dissipative filtering of uncertain singular time-varying delay Markovian jump systems (MJSs) with nonlinear perturbations and generally uncertain transition rates (GUTRs). We focus on the design of a mixed filter, which can include mode-dependent and mode-independent filters in a unified and simple structure. First, a new Lyapunov–Krasovskii functional is proposed through the delay-decomposition approach, and improved Wirtinger-based integral inequalities are used to obtain a sufficient condition to ensure the stochastic admissibility of the considered uncertain nonlinear singular time-varying delay MJSs with dissipative performance. Based on these ingredients, the explicit expression of the desired mixed filter is obtained. Finally, some numerical examples and the filter design of a two-loop circuit network reflect the less conservatism and effectiveness of the method in this article. [ABSTRACT FROM AUTHOR]

With the aid of disturbance observer strategy, this article aims to investigate the disturbance rejection and stabilization problems for periodic piecewise time-varying systems that are subject to time-varying delays, parameter uncertainties, nonlinear perturbations and exogenous disturbances. To be more specific, the periodic piecewise time-varying systems are built by segmenting the fundamental period of periodic systems into a limited number of subintervals. Further, the disturbances engendered from an exogenous system are estimated by deploying the disturbance observer and subsequently, on the premise of disturbance that is esimated, a robust controller protocol is constructed for the considered system. Moreover, by bridging the time-varying periodic piecewise Lyapunov-Krasovskii functional with a matrix polynomial lemma, a set of adequate criteria is framed, which confirms the asymptotic stability of the system that is being addressed. Subsequently, on the premise of established criteria, the design of periodic piecewise gain matrices of devised controller and configured observer are presented. Eventually, the importance and potential of the presented theoretical concepts are evidenced through offering a numerical illustration with the simulation results.

In this paper, a generalized n-species Gilpin–Ayala competition system with saturation effect and nonlinear perturbations is proposed and examined. We first develop a new mathematical technique called “stochastic ϵ -threshold method”, to tackle the nonlinear perturbations and study the competitive coexistence, which includes the existence of ergodic stationary distribution as well as stochastic positive periodic solution. It should be mentioned that the method can be successfully applied to the species coexistence of other biological models. Then, we establish sufficient conditions for exponential extinction of competing species. Finally, several numerical examples are provided to support our theoretical results and analyze the impact of key parameters. [ABSTRACT FROM AUTHOR]

In this paper, we examine an n-species Lotka-Volterra competition system with general infinite distributed delays and nonlinear perturbations. The stochastic boundedness and extinction are first studied. Then we propose a new p-stochastic threshold method to establish sufficient conditions for the existence of stationary distribution ℓ(·). By solving the corresponding Fokker--Planck equation, we derive the approximate expression of the distribution ℓ (·) around its quasi-positive equilibrium. For the stochastic system with periodic coefficients, we use the p-stochastic threshold method again to obtain the existence of positive periodic solution. Besides, the related competition exclusion and moment estimate of species are shown. Finally, some numerical simulations are provided to substantiate our analytical results. [ABSTRACT FROM AUTHOR]

The main concern of this paper is finite-time stability (FTS) for uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD) and multiplicative noise. First, a Lyapunov–Krasovskii function (LKF) is constructed, using the forward difference, and less conservative stability criteria are obtained. By solving a series of linear matrix inequalities (LMIs), some sufficient conditions for FTS of the stochastic system are found. Moreover, FTS is presented for a stochastic nominal system. Lastly, the validity and improvement of the proposed methods are shown with two simulation examples. [ABSTRACT FROM AUTHOR]

This article is focused on the design of an output tracking control scheme for a class of continuous-time periodic piecewise time-varying systems (PPTVSs) with actuator saturation and nonlinear perturbations. The energy-to-peak tracking performance is studied based on an equivalent condition on the definiteness property of matrix polynomials. Considering the actuator saturation and nonlinear perturbation, matrix polynomial-based sufficient conditions are derived through the Lyapunov method using periodic matrix functions. From a perspective of subinterval segmentation aimed at PPTVSs, the proposed conditions can achieve less conservatism for tracking the output of a periodic time-varying reference system, while the controller gains can be computed using convex optimization. Moreover, a heuristic algorithm is constructed to simultaneously guarantee the closed-loop state convergence and the output tracking performance. The reduction in conservatism and the effectiveness of algorithm are demonstrated by illustrative case studies. [ABSTRACT FROM AUTHOR]

This paper studies the convergence behavior of a type of T-S fuzzy system with interval time-varying delay and nonlinear perturbations. A delay partitioning method is used to construct a modified Lyapunov Krasovskii functional(LKF) including triple-integral terms and augmented factors, which is introduced from these equidistant subintervals. In addition, the Free-Matrix-Based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. Eventually, much less conservative results are presented. Numerical analyses are conducted to demonstrate the evaluation of this proposed research development. [ABSTRACT FROM AUTHOR]

This paper deals with the stability and stabilization problems of time-delay systems with nonlinear perturbations. The perturbations are modelled by a nonlinear function of current and/or delayed states. By utilizing Lyapunov–Krasovskii functional, sufficient conditions are obtained in terms of LMIs for the different types of perturbations. The stabilization problem is originally non-convex because of the coupling between the Lyapunov matrices and the controller gains. In order to decouple decision variables, the Young's relation is used in a judicious manner. Numerical examples are given to demonstrate that the proposed method can provide a state feedback controller for a larger delay range than existing methods. [ABSTRACT FROM AUTHOR]

The main concern of this paper is finite-time stability (FTS) for uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD) and multiplicative noise. First, a Lyapunov–Krasovskii function (LKF) is constructed, using the forward difference, and less conservative stability criteria are obtained. By solving a series of linear matrix inequalities (LMIs), some sufficient conditions for FTS of the stochastic system are found. Moreover, FTS is presented for a stochastic nominal system. Lastly, the validity and improvement of the proposed methods are shown with two simulation examples.