Search

This study focuses on the boundedness and stability of the nonlinear hybrid stochastic differential delay equation (NHSDDE) disturbed by Lévy noise (LN). Different from the previous systems with Markovian switching, not only different parameters under different modes, but also different structures under different modes are considered, where a novel Lyapunov function is constructed to handle the impacts of different structures under different modes. Without the linear growth condition, the existence of the global solution is proved for the NHSDDE with LN. Then, the M‐matrix technique is applied to build some reasonable theorems upon the vth moment asymptotic boundedness, the vth moment exponential stability and the almost surely exponential stability for the NHSDDE driven by LN. An approach to solving the admissible upper bound of the time‐delay derivative is given for guaranteeing the asymptotic boundedness and the exponential stability of the global solution. Finally, two numerical examples and homologous simulated outcomes are provided to indicate the usefulness of the presented theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is devoted to solve the quantised control problem of the continuous‐time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities. For the Markov chain, the transition rates are assumed to be partly known. The involved mixed time delays comprise both time‐varying delays and distributed delays. The logarithmic quantiser is introduced in the design of the state feedback controller and the uncertainty is entered into the quantization error matrix represented by an interval matrix. Based on the generalised Itô's formula, the free‐connection weighting matrix method and the stochastic analysis theory, several novel sufficient conditions are derived to guarantee that the trivial solution of the closed‐loop system is robustly exponentially stable in the mean square. Then, the concrete expression form of the desired controller gain is obtained via the solutions to a set of linear matrix inequalities. In addition, the corresponding stability criteria are given for three special situations of Markovian jump systems. Finally, a numerical example and a practical example (the wheeled mobile manipulator) are provided to show the feasibility and availability of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This study is concerned with the non‐fragile set‐membership estimation problem for a class of delayed sensor‐saturated memristive neural networks under the premise of communication protocol transmissions. The exogenous noises are unknown but bounded and the activation function satisfies the sector‐bounded condition. In order to schedule the limited network resources, the node's utilisation right of the communication channel at the current instant is determined by the weighted try‐once‐discard protocol. Besides, the estimator gain perturbations are considered to enhance the robustness of estimation method. The major focus of the study is to a design a non‐fragile estimator such that, for all measurement saturation, mixed time‐delays and estimator gain perturbation, the estimation error exists in the ellipsoid by providing a sufficient criterion and the optimal semi‐axes length of the ellipsoid is found by solving a convex optimisation problem. Finally, a simulation example shows that the proposed non‐fragile estimation strategy is effective. [ABSTRACT FROM AUTHOR]

In this study, the recursive state estimation method based on the event‐triggered protocol is given for time‐varying uncertain complex networks with switching topology (ST), data packet dropouts (DPDs), and randomly occurring non‐linearities (RONs). The event‐triggered strategy is given to regulate the communications and then save the limited network resources when the measurement information is transmitted. The phenomena of RONs, ST, and DPDs are depicted by some random variables obeying the Bernoulli distribution. Besides, the estimator gain perturbations are dealt with. The major aim of this study is to present a new state estimation algorithm for addressed time‐varying uncertain complex networks such that, for all STs, DPDs, and RONs, a minimal upper bound of state estimation error covariance matrix is derived by designing an optimal estimator gain matrix. Finally, a numerical simulation is presented to show the effectiveness of the provided time‐varying state estimation method. [ABSTRACT FROM AUTHOR]