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The problem of $ L_1 $ L 1 output tracking control of positive linear systems in finite time is addressed in this paper. By constructing a linear copositive Lyapunov–Krasovskii functional, some sufficient conditions are achieved to ensure that the states are finite-time bounded and the measurement outputs have $ L_1- $ L 1 − gain performance for given systems, respectively. Next, a state feedback controller is designed to ensure that the output signals of the tracking system can effectively trace the specified signals of reference model with finite-time boundedness and $ L_1 $ L 1 -gain performance. Finally, an example is given to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This article focuses on state and output tracking control for positive continuous-time linear systems without overshoot. Linear state feedback controllers are designed respectively to ensure both the system state, and output can unilateral track the reference state and output. In addition, using Lyapunov direct method, the exponential convergence rate of tracking system is calculated. A numerical example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of positive L1$$ {L}_1 $$ filter for positive Markovian jump systems (PMJSs) with adaptive event‐triggered mechanism and quantization. Considering the mode jump of the system, a new adaptive event‐triggered condition is established, which not only can regulate the communication threshold according to the error of dynamic systems, but also can avoid the asynchronous phenomenon between the system mode and the filter mode. In order to further reduce the burden of communication, a new positive L1$$ {L}_1 $$ filter with the quantized measure system output is developed, and the design condition which ensures the filter error system to be stochastically stable with L1$$ {L}_1 $$ performance is presented which can be solved in terms of linear programming (LP) technique. It is illustrated that there is no Zeno phenomenon. The proposed results are applied to the power allocation in a mobile telecommunication system, and it is shown that compared with the existing results, the event‐triggered filter of this paper has some advantages. [ABSTRACT FROM AUTHOR]

This paper addresses the stochastic stability problem of positive Markov jump linear systems (PMJLSs). A necessary and sufficient condition of stochastic stability for PMJLSs is given which can be checked by solving linear programming feasibility problems due to the positivity property. A common co-positive Lyapunov function is constructed to solve the problem, and the equivalence among stochastic stability, 1-moment stability and exponential mean stability is proved afterwards. Considering the uncertain transition rates situation, PMJLSs with partially known transition rate matrix are investigated, and a necessary and sufficient condition for robust stochastic stability is proposed in linear programming form. Numerical examples are presented to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This study is concerned with H ∞ control problems for positive systems with time delays using dynamic output feedback. Novel bounded real lemma for continuous‐time systems with time delays is first presented, which shows one of the remarkable properties of diagonal positive definite matrix solutions to linear matrix inequalities for positive systems. The proposed results reveal that H ∞ norms of positive systems with time delays in state and output equations are equivalent to that of the corresponding systems with zero delays. The positivity preserving H ∞ control problem by means of dynamic output feedback is also considered, and thus necessary and sufficient conditions in the forms of matrix equalities are established for the solvability of such problem. The desired controller gains can be obtained by means of cone complementarity linearisation techniques. A numerical example is finally given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]