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In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponential stability, which takes into account the transient and steady behaviors of the system, is presented. Second, the relationship between general finite-time mean square stability, finite-time stochastic stability, and quantitative mean square exponential stability is proposed. Subsequently, some sufficient conditions for the existence of state feedback and observer-based controllers are derived, and an algorithm is offered to solve the matrix inequalities resulting from quantitative mean square exponential stabilization. Finally, the effectiveness of the proposed results is illustrated with the numerical example and the practical example. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time contractively bounded control issue for positive linear systems under H ∞ performance. The notion of H ∞ finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the H ∞ finite-time contractive boundedness of the considered positive systems. A state feedback finite-time contractively bounded controller design method is proposed. The corresponding sufficient condition for the existence of the desired controller is derived by using the Lyapunov function method and the matrix inequality technique. Moreover, a computable scheme for solving the controller gain is established by employing the cone complementary linearization approach. Finally, a numerical example and an application example about pest management are used to validate the effectiveness of proposed conditions. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of mixed H 2 / H ∞ control for Itô-type stochastic time-delay systems. First, the H 2 / H ∞ control problem for stochastic time-delay systems is presented, which considers the mean square stability, H 2 control performance index, and the ability of disturbance attenuation of the closed-loop systems. Second, by choosing an appropriate Lyapunov–Krasoviskii functional and using matrix inequality technique, some sufficient conditions for the existence of state feedback H 2 / H ∞ controller for stochastic time-delay systems are obtained in the form of linear matrix inequalities. Third, two convex optimization problems with linear matrix inequality constraints are formulated to design the optimal mixed H 2 / H ∞ controller which minimizes the guaranteed cost of the closed-loop systems with known and unknown initial functions, and the corresponding algorithm is given to optimize H 2 / H ∞ performance index. Finally, a numerical example is employed to show the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time stability of impulsive switched systems. By applying mode-dependent parameter approach and average impulsive switched interval technique, the conditions that guarantee the finite-time annular domain stability and finite-time annular domain boundedness for general linear and nonlinear impulsive switched systems are established. Meanwhile, the superiority of mode-dependent parameter approach over common parameter approach is analysed. Also, we consider the effect of different impulsive strengths and draw a less conservative conclusion. Moreover, we extend the conclusion from nonlinear impulsive switched systems to linear impulsive switched systems, and a new sufficient condition for state feedback controllers is proposed on the basis of coupled matrix inequalities. Furthermore, for systems containing external disturbance, we obtain a sufficient condition of finite-time annular domain boundedness. Finally, we present two examples to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a unified framework for asymptotic and transient behavior of stochastic systems. In order to explain this problem explicitly, a concept of mean square ( γ, α )-stability is first introduced and two stability criteria are derived. By utilizing an auxiliary definition of mean square ( γ , T)-stability, the relations among mean square ( γ, α )-stability, mean square ( γ , T)-stability and finite-time stochastic stability are established. Subsequently, two new sufficient conditions for the existence of state and output feedback mean square ( γ, α )-stabilization controllers are presented in terms of matrix inequalities. A numerical algorithm is given to obtain the relation between γ min  and α . Finally, an example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time annular domain stability and stabilization of stochastic systems, described by an Itô-type differential equation, in which the systems are driven by both Wiener noises and Poisson jumps. First, a new inequality called reverse differential Gronwall inequality is established to achieve less conservative conditions for finite-time annular domain stability. Second, some sufficient conditions are derived to guarantee that the closed-loop system is finite-time annular domain stable by constructing a state feedback controller and an observer-based controller, respectively. All related conditions can be expressed in terms of matrix inequalities and corresponding algorithms are given. Finally, two numerical examples are presented to verify the validity of the derived results, and the effect of Poisson jump intensity on the boundary of the system states is illustrated. [ABSTRACT FROM AUTHOR]