New Results on Delay-Dependent Stability Analysis and Stabilization of Time-Delay Systems

Abstract

The interconnection between physical systems is accomplished by flow of information, energy and material, alternatively known as transport or propagation. As such flows may take a finite amount of time, the reaction of real world systems to exogenous or feedback control signals, from automatic control perspective, are not instantaneous. This results time-delays in systems connected by real-world physical media. Indeed, examples of time-delay systems span biology, ecology, economy, and of course, engineering. To this end, it is known that
an arbitrary small delay may destabilize a stable system whereas, a delay in the controller may be used to stabilize a system that is otherwise not stabilizable by using a delay-free controller. In general, the presence of time-delay in a system makes the system dynamics infinite-dimensional, and analysis of such systems is complex.This thesis investigates stability analysis and stabilization of time-delay systems. It proposes a delay-decomposition approach for stability analysis of systems with single delay that leads to a simple LMI condition using a Lyapunov-Krasovskii functional. Moreover, a static state feedback controller is designed for systems with state and input-delay using this delay-decomposition approach. Numerical comparison of the present results vis-`a-vis the existing ones for the systems with constant delay considered shows that the present ones are superior. Next, a PI-type controller is implemented for systems with input-delay to improve the tolerable delay bound. Other problems considered is to analyze the stability of systems with two delays. As the number of delays incorporated in the system dynamics increases, it becomes further complex for analysis.