Certain investigation on delay dependent stability of a class of dynamical systems with time delays

Abstract

The stability study of dynamical systems with time delays (time-varying/time-invariant) has been more active research area during the last decade, since many dynamical systems can be modelled into delay differential equations. Time-delay systems have been widely applied successfully in Networked Control Systems (NCS) such as thermal control system, DC motor speed control system, load frequency control system, generator excitation control system, mechanical translational system, power system, etc,. The problem of delay-dependent stability of dynamical system with time-delays based on characteristic Equation, Lyapunov-Krasovskii (LK) functional and Linear Matrix Inequality (LMI) technique has been considered in this thesis. In first part of thesis, the stability of time-delayed closed loop dynamical system under networked environment is analyzed. The measurement unit and communication links used by networked control system (NCSs) cause a significant amount of time delays in feedback closed loop system. These delays deteriorate the performance of the closed loop system paving way for system instability. Let considered, two different techniques are presented to obtain the stable delay region: they are characteristic Equation method and LMI based approach. The characteristic Equation method is an analytical method based on the transcendental characteristics of the Equation. The stable delay region is the maximum amount of time-delay that the control system can tolerate before it becomes unsteady. Foremost, without using any estimation, the transcendental polynomial Equation is converted into a new polynomial without the transcendentality such that real poles of new polynomial exactly coincide with the imaginary roots of the characteristic Equation. newline newline newline