Wei-Chau Xie

Input-to-state stability of impulsive and switching hybrid systems with time-delay

This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive and switching hybrid systems with time-delay, using the method of multiple Lyapunov-Krasovskii functionals. It is shown that, even if all the subsystems governing the continuous dynamics, in the absence of impulses, are not ISS/iISS, impulses can successfully stabilize the system in the ISS/iISS sense, provided that there are no overly long intervals between impulses, i.e., the impulsive and switching signal satisfies a dwell-time upper bound condition. Moreover, these impulsive ISS/iISS stabilization results can be applied to systems with arbitrarily large time-delays. Conversely, in the case when all the subsystems governing the continuous dynamics are ISS/iISS in the absence of impulses, the ISS/iISS properties can be retained if the impulses and switching do not occur too frequently, i.e., the impulsive and switching signal satisfies a dwell-time lower bound condition. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.

Brief paper: Stochastic consensus seeking with communication delays

This paper investigates the consensus problem of dynamical networks of multi-agents where each agent can only obtain noisy and delayed measurements of the states of its neighbors due to environmental uncertainties and communication delays. We consider general networks with fixed topology and with switching (dynamically changing) topology, propose consensus protocols that take into account both the noisy measurements and the communication time-delays, and study mean square average-consensus for multi-agent systems networked in an uncertain environment and with uniform communication time-varying delays. Using tools from differential equations and stochastic calculus, together with results from matrix theory and algebraic graph theory, we establish sufficient conditions under which the proposed consensus protocols lead to mean square average-consensus. Simulations are also provided to demonstrate the theoretical results.

Impulsive stabilization of stochastic functional differential equations

Abstract This paper investigates impulsive stabilization of stochastic delay differential equations. Both moment and almost sure exponential stability criteria are established using the Lyapunov–Razumikhin method. It is shown that an unstable stochastic delay system can be successfully stabilized by impulses. The results can be easily applied to stochastic systems with arbitrarily large delays. An example with its numerical simulation is presented to illustrate the main results.

Exponential stability of a class of complex-valued neural networks with time-varying delays

This paper studies a class of complex-valued neural networks with time-varying delays. By using the conjugate system of the complex-valued neural networks and Brouwer?s fixed point theorem, sufficient conditions to guarantee the existence and uniqueness of an equilibrium are obtained. Some criteria on globally exponential stability of the equilibrium of the complex-valued neural networks are also established by using a delay differential inequality. These results are easy to apply to the study of the complex-valued neural networks whether their activation functions are explicitly expressed by separating their real and imaginary parts or not. Two examples with numerical simulations are given to highlight the effectiveness of the obtained results.

Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations

In this paper, we investigate the dynamical behavior of a class of delayed neural networks with discontinuous neuron activations and general mixed time-delays involving both time-varying delays and distributed delays. Due to the presence of time-varying delays and distributed delays, the step-by-step construction of local solutions cannot be applied. This difficulty can be overcome by constructing a sequence of solutions to delayed dynamical systems with high-slope activations and show that this sequence converges to a desired Filippov solution of the discontinuous delayed neural networks. We then derive two sets of sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of linear matrix inequalities (LMIs) and M-matrix properties (equivalently, some diagonally dominant conditions), respectively. Convergence behavior of both the neuron state and the neuron output are discussed. The obtained results extend previous work on global stability of delayed neural networks with Lipschitz continuous neuron activations, and neural networks with discontinuous neuron activations and only constant delays.

Existence, continuation, and uniqueness problems of stochastic impulsive systems with time delay

This paper studies stochastic impulsive systems with time delay, where the impulse times are state-dependent. Using Ito calculus, we develop the essential foundation of the theory of the mentioned system. In particular, we establish results on local and global existence, forward continuation, and uniqueness of adapted solutions.

Buckling mode localization in rib-stiffened plates with randomly misplaced stiffeners

Abstract Buckling mode localization in rib-stiffened rectangular plates with randomly misplaced stiffeners is studied in this paper. Localization factors, which characterize the average exponential rates of growth or decay of amplitudes of deflection, are determined using the method of transfer matrix. The smallest positive Lyapunov exponent of the corresponding discrete dynamical system is the localization factor of interest. For a plate simply supported at the rib-stiffeners, the buckling behaviour of the plate is similar to that of a multispan continuous beam. The effect of misplacement of the rib-stiffeners on buckling mode localization increases with the increase of the flexural rigidities of the stiffeners. The larger the values of the torsional rigidities of the rib-stiffeners, the larger the values of the localization factors and the degrees of localization in the buckling modes.

Exponential stability of switched stochastic delay systems with non-linear uncertainties

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results.

On the (h0,h)-stabilization of switched nonlinear systems via state-dependent switching rule

Abstract This paper considers switching stabilization of some general nonlinear systems. Assuming certain properties of a convex linear combination of the nonlinear vector fields, two ways of generating stabilizing switching signals are proposed, i.e., the minimal rule and the generalized rule, both based on a partition of the time-state space. The main theorems show that the resulting switched system is globally uniformly asymptotically stable and globally uniformly exponentially stable, respectively. It is shown that the stabilizing switching signals do not exhibit chattering, i.e., two consecutive switching times are separated by a positive amount of time. In addition, under the generalized rule, the switching signal does not exhibit Zeno behavior (accumulation of switching times in a finite time). Stability analysis is performed in terms of two measures so that the results can unify many different stability criteria, such as Lyapunov stability, partial stability, orbital stability, and stability of an invariant set. Applications of the main results are shown by several examples, and numerical simulations are performed to both illustrate and verify the stability analysis.

Class-KL estimates and input-to-state stability analysis of impulsive switched systems☆

Abstract In this paper, we investigate input-to-state stability of impulsive switched systems. The goal is to bridge two apparently different, but both useful, stability notions, input-to-state stability and stability in terms of two measures, in the hybrid systems setting. Based on two class- KL function estimates and a comparison theorem for impulsive differential equations, two sets of sufficient Lyapunov-type conditions for input-to-state stability in terms of two measures are obtained for impulsive switched systems. These conditions exploit some nonlinear integral constraints in terms of generalized dwell-time conditions to balance the continuous dynamics and impulsive dynamics so that input-to-state stability is achieved, despite possible instability of individual continuous subsystems or destabilizing impulsive effects. An illustrative example is presented, together with numerical simulations, to demonstrate the main results.