Robustness with respect to small delays for exponential stability of non-autonomous systems

Abstract

Robustness of stability with respect to small delays, e.g., motivated by feedback systems in control theory, is of great theoretical and practical important, but this property does not hold for many systems. In this paper, we introduce the conception of robustness with respect to small time-varying delays for exponential stability of the non-autonomous linear systems. Sufficient conditions are given for the non-autonomous systems to be robust, and examples are provided to illustrate that the conditions are satisfied for a large class of the non-autonomous parabolic systems.

An Improved PID Controller for the Compliant Constant-Force Actuator Based on BP Neural Network and Smith Predictor

“…there is a pure time delay link in the pneumatic systems based on pneumatic cylinders [22]. In the implementation of such stabilizing feedback control, even a small time delay may cause destabilization of the controller [23], because the time delay makes the controlled variables unable to reflect the disturbance of the system in time, which will produce a larger overshoot and longer adjustment time [24].…”

On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions

“…It is therefore of vital importance to understand the effects of small time delays to the dynamical behavior of the system. This problem is relatively well understood for finite-dimensional linear systems, see [18,22]. Related results and infinite-dimensional extensions can be found in [1,13,24,22,48,50], etc.…”

Robustness of Exponential Dissipation with respect to Small Time Delay

“…Mathematically, it is also very important to understand the sensitivity of the dynamical behavior of the system to the introduction of small time delays. For linear systems, we well understand this problem, including both finite dimensional and infinite dimensional situations, see [1][2][3][4][5]. However, for nonlinear systems, the problem is much more difficult, but there are some very nice results in [6][7][8][9][10].…”