Robust Stability of Linear Delay Systems

Abstract

Difference always exists between a real dynamic system and its mathematical model because of the simplification in modeling, the measurement errors of system parameters, and so on. It is very natural, hence, to study the dynamic systems governed by differential equations involving a number of uncertain parameters. In practice, a dynamic system should be robust stable. The problem of robust stability of linear dynamic systems can be roughly stated as follows. Given a family Ω of linear dynamic systems and a set D on the complex plane, how to construct a computationally tractable technique to determine whether the characteristic roots of every system in Ω fall into D. This problem is usually referred to as the D-stability of Ω. For the stability analysis of a continuous-time dynamic system, D should be the open left half-plane of the complex plane, whereas D should be an open unite circular disk on the complex plane for the stability analysis of a discrete-time dynamic system. As a special, but very important case of D-stability, a system is said to be interval stable if it is asymptotically stable under all parameter combinations when some uncertain parameters vary on their pre-specified intervals respectively.