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This paper presents an adaptive event-triggered filter of positive Markovian jump systems based on disturbance observer. A new adaptive event-triggering mechanism is constructed for the systems. A positive disturbance observer is designed for the systems to estimate the disturbance. A distributed output model of each subsystem of positive Markovian jump systems is introduced. Then, an adaptive event-triggering distributed filter is designed by employing stochastic copositive Lyapunov functions. All presented conditions are solvable in terms of linear programming. Under the designed disturbance observer and the distributed filter, the corresponding error system is stochastically stable. The filter design approach is also developed for discrete-time positive Markovian jump systems. The contribution of the paper lies in that: (i) A new adaptive event-triggering mechanism is established for positive systems, (ii) A positive disturbance observer is designed for the disturbance of positive Markovian jump systems, and (iii) The designed distributed filter can guarantee the stochastic stability of the error while existing filters in literature only achieve the stochastic gain stability of the error. Finally, two examples are given to illustrate the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus of discrete-time positive multi-agent systems. A framework on the consensus of positive multi-agent systems is constructed. By introducing a finite point and a self-feedback term, a novel consensus protocol is proposed to drive all states to common nonnegative finite values. An improved error model is established for positive multi-agent systems. Based on the consensus error model, the consensus of the agents is transformed into the stability of the error systems. Under the proposed consensus protocol and the new consensus error model, the consensus of agents is realized. A copositive Lyapunov function is chosen to derive the consensus of the multi-agent systems. Such a consensus approach is extended for time-delay multi-agent systems. All positivity and consensus conditions can be solved by virtue of linear programming. The main novelties of this paper lie in that: (i) A novel consensus error model is established, (ii) A finite value consensus is achieved, and (iii) Linear programming-based conditions are presented for the consensus design. Finally, two illustrated examples are given to verify the validity of the theoretical findings. • A novel consensus error model is established for PMASs. • A finite value consensus is achieved under the presented consensus framework. • Linear programming and copositive Lyapunov function are chosen as the computation and analysis approaches. [ABSTRACT FROM AUTHOR]

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]

This paper is concerned with the design of event-triggered controller for positive Takagi-Sugeno (T-S) fuzzy systems with a random time-delay. The random time-delay is described as a Markov process. A controller switched at different event-triggered instant is proposed. By constructing a new event-triggered instant-dependent linear co-positive Lyapunov function, the design criteria of event-triggered controller is derived to ensure the positivity and stability of the closed-loop system. These criteria can be solved by linear programming (LP) technique. A positive lower bound on the inter-execution time is ensured, which means that there is Zeno-free phenomenon. Finally, the simulation has demonstrated the effectiveness and merit of the proposed results. [ABSTRACT FROM AUTHOR]

This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design. [ABSTRACT FROM AUTHOR]

This paper investigates L 1 -gain analysis and control of impulsive positive systems (IPSs) with interval uncertainty and time delay. For different types of impulsive effect, by means of the Razumikhin techniques and Lyapunov function theory, conditions are developed for guaranteeing the robust exponential stability with L 1 -gain performance. Then the positive stabilization with L 1 -gain performance is also addressed for IPSs with interval uncertainty and time delay through the state feedback control. In addition, the way to explore the minimum L 1 -gain is discussed. All the obtained conditions can be easily inspected by the linear programming (LP) method when some parameters are preset. Finally, simulations are provided to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l 1 performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l 1 -gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results. [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]

This paper is concerned with robust model predictive control for positive systems. The technique of model predictive control is extended to the context of positive systems. By using the linear copositive Lyapunov function approach, a robust model predictive controller for positive systems is first constructed. Being unlike the classic robust control with ℓ 2 -gain performance, the robustness of the underlying systems is guaranteed by means of ℓ 1 -gain performance. In order to increase the feasibility of the present conditions, a multi-step control strategy is then utilized. Accordingly, a cone invariant set is addressed to satisfy the recursive feasibility of the present design. All present conditions can be described by linear programming. Meanwhile, the main computation of these conditions is completely off-line, by which the computational burden is reduced. Finally, an illustrative example is given to show the effectiveness of the design. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the problem of stabilization by state feedback control of Takagi–Sugeno (T–S) fuzzy discrete-time systems with multiple fixed delays while imposing positivity in closed-loop. The obtained results are presented under linear programming (LP) form. In particular, the synthesis of state feedback controllers is first solved in terms of Linear programming for the unbounded controls case. This result is then extended to the stabilization problem by nonnegative controls, and stabilization by bounded controls. The stabilization conditions are derived using the single Lyapunov–Krasovskii functional (LKF). An example of a real plant is studied to show the advantages of the design procedure. A comparison between linear programming and LMI approaches is presented. [Copyright &y& Elsevier]