Jitao Sun

Brief paper: Controllability of Boolean control networks with time delays in states

This paper investigates the controllability of Boolean networks with time-invariant delays in states. After a brief introduction on converting the logic dynamics to discrete time delay systems, the controllability via two kinds of controls is studied. One kind of control is generated by Boolean control networks, another kind of control is free Boolean sequences. In both cases, necessary and sufficient conditions of the controllability of Boolean control networks are proved. Finally, examples are given to illustrate the efficiency of the obtained results.

p-Moment stability of stochastic differential equations with impulsive jump and Markovian switching

This paper introduces some new concepts of p-moment stability for stochastic differential equations with impulsive jump and Markovian switching. Some stability criteria of p-moment stability for stochastic differential equations with impulsive jump and Markovian switching are obtained by using Liapunov function method. An example is also discussed to illustrate the efficiency of the obtained results.

Brief paper: Controllability of probabilistic Boolean control networks

This paper deals with the controllability of probabilistic Boolean control networks. First, a survey on the semi-tensor product approach to probabilistic Boolean networks is given. Second, the controllability of probabilistic Boolean control networks via two kinds inputs is studied. Finally, examples are given to show the efficiency of the obtained results.

Asymptotic stability of differential systems with impulsive effects suffered by logic choice

In this paper, we investigate the asymptotic stability of differential systems with impulsive effects suffered by logic choice. First, we give the expression of system with logic selected impulsive effects, which is a hybrid system. Second, by using semi-tensor product, a criterion of asymptotic stability for the system is provided. Third, we study the linearly coupled system with impulsive effects under logic choice and give a sufficient condition for asymptotic stability. Finally, a numerical simulation is given to illustrate the effectiveness of our results.

Brief paper: Complete controllability of impulsive stochastic integro-differential systems

This paper is concerned with the controllability of impulsive stochastic integro-differential systems. Sufficient conditions of complete controllability for impulsive stochastic integro-differential systems are obtained by using Schaefers fixed point theorem. A numerical example is provided to show the effectiveness of the proposed results.

Output controllability and optimal output control of state-dependent switched Boolean control networks

In the present paper, we investigate the output-controllability and optimal output control problems of a state-dependent switched Boolean control network. By using the semi-tensor product, the algebraic form of the system is obtained. Then, output-controllability problems of the system are discussed and some necessary and sufficient conditions are given. Next, the Mayer-type optimal output control issue is considered and an algorithm is provided to find out the control sequence. At last, an example is given to show the effectiveness of the main results.

Technical communique: Stabilization of discrete-time Markovian jump linear systems via time-delayed and impulsive controllers

This paper discusses the stabilization problem for a class of discrete-time Markovian jump linear systems with time-delayed and impulsive controllers. The delay in the mode signal is assumed to be constant, while that in the system state may be time-varying. First, a hybrid controller with delay and impulses is introduced for the discrete-time stochastic systems. Then, some sufficient conditions are proposed for the design of a hybrid controller such that the closed-loop system is stochastically stable. Finally, a numerical example is provided to illustrate the effectiveness of the proposed result.

On hybrid control of a class of stochastic non-linear Markovian switching systems

In this paper, we address the problem of hybrid control for a class of stochastic non-linear Markovian switching systems. First, a hybrid controller is introduced for the systems. Then under some appropriate assumptions, the stabilization condition for the systems under pure impulsive control is given. Further under impulsive control, the output feedback stabilization problem of the systems is discussed and linear output feedback controllers are designed. Finally a numerical example is provided to illustrate the effectiveness of the proposed methods.

Observability and detectability of discrete-time stochastic systems with Markovian jump

Abstract This paper studies detectability and observability of Markov jump discrete-time linear stochastic systems with multiplicative noise (MJDLS for short). The relations between some concepts of detectability and observability are established. These relations, together with equivalent expressions of observability Gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability. As applications, discrete-time stochastic Lyapunov equations and stochastic discrete algebraic Riccati equations (SDARE) are discussed.

Approximate controllability of stochastic impulsive functional systems with infinite delay

This paper studies the approximate controllability of stochastic impulsive functional system with infinite delay in abstract space. By using the contraction mapping principle, some sufficient conditions are given with no compactness condition imposed on the semigroup generated by the linear part of the system. Then with the help of the Nussbaum fixed point theorem, the restriction of the combination of system parameters is dropped. Finally, an example is shown to illustrate our results.