Abstract We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by splitting space domains. However, we take into account approximation errors during stability analysis. Using a quadratic Lyapunov function, we obtain a suff...

For an evolution family on the half-line U = (U(t; s)) ts0 of bounded linear operators on a Banach space X we introduce operators G 0 ; G X and I X on certain spaces of X-valued continuous functions connected with the integral equation u(t) = U(t; s)u(s) + R t s U(t;)f()dd: We characterize exponential stability, exponential expansiveness and exponential dichotomy of U by properties of G 0 ; G X...

In this paper, the exponential stability and the L2 induced gain performance are investigated for a collection of plants whose feedback control loops are closed via a shared network link. Due to a limited communication capacity, the network link can only close one feedback control loop at a time, while the other control loops are assumed to be open-loop. Therefore, it is necessary to carefully ...

In this paper, global uniform exponential stability of perturbed dynamical systems is studied by using Lyapunov techniques. The system presents a perturbation term which is bounded by an integrable function with the assumption that the nominal system is globally uniformly exponentially stable. Some examples in dimensional two are given to illustrate the applicability of the main results.

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the...

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 deriv...