Strong stabilization of time delay systems

Abstract

The objective of this thesis is to investigate the problem of finding a proper rational stable controller stabilizing an unstable time-delay system. In order to achieve this objective two approaches were suggested. In the first approach, time-delay element was approximated using different techniques for time-delay approximation. The approximation techniques used are (1st, 2nd, and 3rd) order Padé, 2 nd order Laguerre, and 2nd order Kautz. Then, the problem of stabilizing a time delay system by a rational, stable controller was formulated as an H∞-interpolation problem. The Nevanlinna-Pick (N-P) algorithms for distinct, repeated at infinity, and complex interpolation points were used. An algorithm for twice real repeated interpolation points was developed and used. Then, the stable controller was found from the interpolation function. Simulation using Matlab Simulink was used to test for stability. The 2nd approach was based on earlier result from literature, where a time-delay system is transformed into a two-dimensional system. Then, a necessary and sufficient condition for existence of irrational stable controller, which may be approximated by a stable rational controller, was proved, but no tractable algorithm for finding such controller was reported. (Abstract shortened by UMI.)