Search

This paper investigates the problem of absolute exponential stability analysis for switching time-delay Lurie system (STDLS) with all modes unstable. By proposing a novel switching time-varying Lyapunov-Razumikhin function, a computable sufficient condition is formulated to guarantee absolute exponential stability of STDLS under mode-dependent range dwell-time (MDRDT) switching. Especially, theoretical results are applied to switching delay Hopfield neural network. Simulations are served to illustrate the developed theory. [ABSTRACT FROM AUTHOR]

In this paper, stability analysis and stabilization control of discrete-time impulsive switched time-delay systems with all unstable subsystems are discussed. By utilizing a switching time-varying Lyapunov-Krasovskii functional and the mode-dependent interval dwell-time switching rule, we derive some more general stability theorems for the considered time-delay system with all subsystems being unstable. Moreover, we design a time-varying state feedback controller to ensure the stabilization of the resulting closed-loop system. Eventually, the theoretical findings are demonstrated utilizing numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the functional dynamic equation of second order is studied on an arbitrary time scale under milder restrictions without the assumed conditions in the recent literature. The Nehari, Hille, and Ohriska type oscillation criteria of the equation are investigated. The presented results confirm that the study of the equation in this formula is superior to other previous studies. Some examples are addressed to demonstrate the finding.

This paper focuses on the problem of state estimation for certain switched time-varying systems with time-varying delay and nonlinear disturbance. By using an integral inequality technique and a method used in positive systems, we have established several explicit criteria for state estimation of the system, which reduce to stability criteria for some particular cases. The involved nonlinear disturbance of the system takes more general form including both the internal disturbance and the external disturbance. Three numerical examples are also given to verify the validity of the obtained theoretical results.

This paper studies consensus and \(H_\infty\) consensus problems for heterogeneous multi-agent systems composed of first-order and second-order integrator agents. We first rewrite the multi-agent systems into the corresponding reduced-order systems based on the graph theory and the reduced-order transformation. Then, the linear matrix inequality approach is used to consider the consensus of heterogeneous multi-agent systems with time-varying delays in directed networks. As a result, sufficient conditions for consensus and \(H_\infty\) consensus of heterogeneous multi-agent systems in terms of linear matrix inequalities are established in the cases of fixed and switching topologies. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.

We investigate the problem of reachable set bounding for a class of continuous-time and discrete-time nonlinear time-varying systems with time-varying delay. Unlike some preceding works, the involved disturbance input and time-varying delay are not assumed to be bounded. By employing an approach which does not involve the conventional Lyapunov-Krasovskii functional, new conditions are proposed such that all the state trajectories of the system converge asymptotically within a ball. Two illustrative examples are also given to show the effectiveness of the obtained results.