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This paper studies the problem how to estimate the reachable set for a class of delayed bidirectional associative memory neural network systems (NNSs), which have Markov switching parameters and unit-energy or unit-peak bounded disturbance inputs. The feature of the Markov jump bidirectional associative memory NNSs shows in the following twofold: the time delay is time varying; the transition rates is time varying. Moreover, the time-varying transition rates is piecewise constant. Using the Lyapunov functional method, delay-partitioning and linear matrix inequalities techniques, the estimate problem of the reachable set depending on time delay is solved. The effectiveness of the given results is illustrated by the proposed numerical examples. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of dissipative filtering for a class of nonlinear singular Markovian Jump systems (SMJSs) with time-varying delays. Our consideration is centered on the design of a mixed filter that can contain both mode-dependent and mode-independent filters in a unified framework. By using a delay-decomposition approach and constructing a mode-dependent stochastic Lyapunov–Krasovskii functional, sufficient delay-dependent conditions are derived in terms of linear matrix inequalities, which guarantee the considered nonlinear SMJSs to be stochastically admissible with a dissipativity performance γ . Based on the conditions, the existence conditions and parameters of the desired filter are obtained. Two numerical examples are given to illustrate the reduced conservatism and the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of the disturbance observer based control for a class of continuous-time uncertain systems subject to input saturation and nonlinearity. The input of the system includes two parts, the control input and the disturbance input. The nonlinearity of the system, which satisfies a global Lipschitz condition, is considered as two cases of known nonlinearity and unknown nonlinearity. By virtue of the technique of the disturbance observer based controller, the anti-disturbance controllers are designed respectively with both the polytopic and dead-zone representations of the saturation function, which ensure that the resulting closed-loop systems are asymptotically stable with an estimation of the domain of attraction described by the level set of the Lyapunov function. Further, an iterative optimization method is used to obtain the maximum estimation of the domain of the set of initial states. An example of application design for a flight control system illustrates the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of non-fragile and mode-dependent $$H_{\infty }$$ filter design for a class of nonlinear stochastic Markovian jump systems with mode-dependent time-varying delays and norm-bounded parameter uncertainties. The non-fragile and mode-dependent filter to be designed is assumed to include multiplicative gain variations which result from inaccuracies in filter implementation, and the desired filter ensures the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed $$H_{\infty }$$ -norm level for all admissible uncertainties. A stochastic Lyapunov-Krasovskii function is proposed to reflect the information of Markovian jump modes and the mode-dependent time-varying delays, and a set of strict linear matrix inequalities are utilized to derive sufficient conditions that guarantee the desired filter can be constructed. A numerical example and a vertical take-off and landing (VTOL) helicopter system are utilized to illustrate the effectiveness and usefulness of the main results obtained. [ABSTRACT FROM AUTHOR]

This work investigates the dissipativity and stability analysis problems for Markov jump generalized neural networks subject to time-varying interval delays. The aim of the present study is to determine whether the new dissipativity and stability criteria with less conservatism could be established for Markov jump generalized delayed neural networks or not. In this connection, a more general dissipative property index inequality is firstly introduced. On basis of fully considering mode-dependent matrices in the Lyapunov–Krasovskii functional, some advantageous negative terms ignored in some existing works are taken into account. By employing some novel integral inequalities and stochastic analysis theory, some available less conservative criteria are developed. Three compared examples are finally shown to explain the reduced conservatism and superiority of the presented criteria for Markov jump generalized delayed neural networks. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the adaptive finite-time flocking problem for a class of second-order nonlinear multi-agent systems with parameter uncertainties. The states of all agents can achieve finite-time consensus by using the proposed control algorithm under an undirected graph. It is shown that connectivity preservation is guaranteed by choosing an appropriate Lyapunov potential function. A numerical example is presented to illustrate the effectiveness of the proposed consensus protocol. [ABSTRACT FROM AUTHOR]