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The output feedback l 1 control problems of positive Markov jump systems(PMJSs) are studied using event-triggered method in this paper. Firstly, two novel dynamic output event-triggered control strategies(DOETCS) are proposed for continuous-time PMJSs as well as discrete-time PMJSs, which can reduce the event-triggered frequency and save network resources. Then, by constructing multiple linear copositive Lyapunov functions, two sufficient conditions about positivity and stochastic stability with l 1 -gain performance are presented for the continuous-time closed-loop PMJSs and the discrete-time closed-loop PMJSs. Simultaneously, two desired output feedback l 1 controllers and two DOETCS are also co-designed to stabilize the PMJSs in continuous and discrete cases, respectively. All the conditions obtained in this paper are in the form of linear programming(LP). Further more, the influence of parameters in the novel DOETCS on the event-triggered frequency is investigated in detail in the section of numerical simulation. Finally, two numerical examples are provided to verify the effectiveness of the proposed design schemes. [ABSTRACT FROM AUTHOR]

A novel memory event-triggered scheme for positive systems is proposed in this paper. To address the conservatism of the existing memory event-triggered scheme, the weight parameter on the left side of the memory event-triggered scheme is replaced with a dynamic function. This modification results in a dynamic weighted memory event-triggered scheme that can be applied in both continuous-time and discrete-time contexts. By adjusting the weight dynamically based on the system operation, the scheme can respond more effectively to changes in the system state. Compared to the memory event-triggered scheme, a more flexible balance is achieved between improving system performance and saving system resources. A joint design that combines the dynamic weighted memory event-triggered scheme and positive systems is presented for continuous linear systems, with the controller gain obtained by a linear programming strategy. The proposed co-design scheme is subsequently extended to discrete positive systems. To demonstrate the effectiveness of the proposed method, two practical applications are presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with positivity and stochastic stability of a class of positive singular Markovian jump time-delay systems with partially unknown transition rates. First, a necessary and sufficient condition is established to check the positivity of singular Markovian jump time-delay systems. By constructing an appropriate linear co-positive Lyapunov–Krasovskii function, a sufficient condition of stochastic stability for positive singular Markovian jump time-delay systems is established, which can be solved in terms of linear programming. Based on the results obtained, we give a necessary and sufficient condition of stability for normal positive Markovian jump systems and build some relationships with some existing results. Finally, three numerical examples are used to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]