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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 is concerned with the robust stability of uncertain neutral-type Lur'e system with time-varying delays and sector bounded nonlinearities. By constructing a modified Lyapunov-Krasovskii functional (LKF), some new robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) without using the general free-weighting matrix method. The criteria are less conservative and more efficiently calculative than some previous ones. Four numerical examples are presented to show the effectiveness and merits of the proposed approach. [ABSTRACT FROM AUTHOR]

This technical note studies the problem of exponential estimates for Markovian jump systems with mode-dependent interval time-varying delays. A novel Lyapunov–Krasovskii functional (LKF) is constructed with the idea of delay partitioning, and a less conservative exponential estimate criterion is obtained based on the new LKF. Illustrative examples are provided to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This work considers the design of nonfragile H ∞ observer-based controller for nonlinear networked control systems (NCSs) subject to multipath packet dropouts. The nonlinear NCSs are modeled through the Takagi–Sugeno (T–S) fuzzy model. The occurrences of packet dropouts in the measurable output and the control input indicate the multipath packet dropouts. Two random sequences which are mutually independent and obey the Bernoulli distribution are adopted to represent the multipath packet dropouts. Unlike most existing works about the observer-based controller design, a novel observer design scheme is developed in this paper for the T–S fuzzy NCSs with packet dropouts, which does not require the observer to be designed to share the same local system parameters " A l " as the fuzzy plant. Then, by means of the Lyapunov function approach, sufficient conditions are developed to make certain that the controlled T–S fuzzy NCSs are stochastically stable with a H ∞ performance index. Through adopting a two-step design method, the search for the local system parameters and gains of the observer and the controller gains is formulated as a feasibility problem of linear matrix inequalities (LMIs). Eventually, the effectiveness of the derived results is verified by an example. • The observer cannot always obtain the local system parameters of the T-S fuzzy plant. • A new observer design scheme is developed for T-S fuzzy plant with packet dropouts. • By using the two-step design scheme, the conditions are expressed as strict LMIs. [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 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]