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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]

Summary: In this work, the problem of adaptive state regulation is addressed via output feedback for a wide class of large‐scale systems with strongly interconnected time‐delay nonlinearities. A design approach of partially decentralized adaptive controller is proposed, which gives a novel pair of reduced‐order observer and controller with nonidentifier‐based double adaptive gains. Compared with the existing results, the growth restrictions imposed on the interconnections are relaxed, where the growth rate includes not only an unknown constant but also the nonpolynomial functions of system output. The double dynamic gains are capable of compensating both the uncertain nonpolynomial growth rate and the unknown time‐varying delay. By constructing novel Lyapunov–Krasovskii functionals and combining dynamic‐scaling technique with Barbălat's lemma, it is shown that global adaptive state asymptotical regulation is achieved, that is all the closed‐loop signals are bounded, and the states of system and observer tend to zero as time goes to infinity. Finally, a simulation example is given to illustrate the proposed control scheme is independent of time delay and well universal. [ABSTRACT FROM AUTHOR]

This study addresses the positive filter design problem for continuous‐time positive Markov jump linear systems (PMJLSs). Based on the necessary and sufficient condition for L1 ‐gain performance, two sufficient conditions to design positive full‐order and reduced‐order L1 ‐filters for PMJLSs are provided in terms of linear programming, respectively. A practical numerical example of an isotropic, homogeneous and unidimensional aquifer is presented at last to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

This study introduces a problem of positive L1 filter design for positive piecewise homogeneous Markovian jump Takagi–Sugeno (T–S) fuzzy systems. The difference between the existing achievements is that the considered transition rate of the positive Markovian jump system is time‐varying. This time‐varying nature is finite piecewise homogeneous. The time variation of the transition rate is characterised by two cases: stochastic variation and arbitrary variation. First of all, sufficient conditions are obtained for stochastic stability and L1 performance under the transition rate in a manner of stochastic variation and arbitrary variation by means of choosing a linear co‐positive Lyapunov function. Then, based on the obtained achievements, the problem of positive L1 filter design for the positive piecewise homogeneous Markovian jump T–S fuzzy system is studied. All the mentioned problems in this study can be solved by linear programming. Finally, a biological model is proposed to illustrate the effectiveness of theoretical 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]

This paper deals with a synchronization problem of a class of neutral-type complex dynamic networks with interval time-varying coupling delays under a pair of nonlinear constraints. Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities ( LMIs) based on a modified Lyapunov- Krasovskii ( LK) functional approach. By a convexity analysis of the matrix function, a free-weighting matrix method is employed for the purpose of reducing the conservatism of the existing results. Two illustrative examples are given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]