TIME-DELAY CONTROL USING CONIC SECTORS

Abstract

Time delays exist in many practical systems and ignoring them could degrade systems performance and even lead to instability. That’s why it’s of vital importance to study the stability and how to control systems with time delays. The main contribution of this thesis is to provide a novel way of establishing conic bounds for stable LTI systems with time-varying state delays. Two linear matrix inequality conditions are provided. Alone, they can be used as an analysis tool, determining conic bounds for LTI systems subject to bounded time-varying state delays. Combined with the Conic Sector Theorem, the conic bounds established by the LMIs can be used directly to design conic controllers, ensuring the close-loop I-O stability.Background knowledge about linear undelayed systems is reviewed, including the state-space equations, stability, controllability, and observability. The optimal state- feedback control problem is stated. Time-delays are then introduced into the system. The Lyapunov-Krasovskii based method and the input-output approach are discussed. The conic sector theorem is also stated as the basis of the main result. This document is formulated in the following order. Chapter I gives the introduction, containing the motivation of this study, a review of notations, definitions, theorems, and some background knowledge. Chapter II provides a literature review. Five papers were chosen to be studied in detail and a comparative study was conducted. Numerical examples were given to show the results. Chapter III implements the main results of the author’s original work.