The proposed project deals with various problems of analysis and design of control systems subject to parametric uncertainty. Specifically we consider interval systems whose transfer function coefficients are linear or multilinear functions of the parameters subject to perturbation. The main goals of this project are 1) to develop effective methodologies to design controllers that perform satisfactorily under large amounts of parametric uncertainties and 2) to expand understanding of time and frequency domain properties of various types of control systems. The project consists of two parts: development of new theory and its implementation as a computer aided design software package. The theoretical problems we propose to solve are as follows: 1) Reexamining the classical control design and analysis techniques with robustness ingredients and developing new design methodologies for robust parametric control design. 2) Developing relevant theory for time delay systems. This includes what is a necessary and sufficient condition to determine robust stability of a time delay interval system with a fixed controller, how to computationally check the robust stability, what are the frequency and time domain characteristics of a time delay interval system, and how to adjust selective parameters within their intervals to improve the system performance. 3) Developing equivalent theory and computational algorithms to deal with multilinear interval systems. 4) Developing theory to examine the time domain properties of interval systems and its use in controlling transient response. 5) Developing a new modeling and identification technique to determine an interval system from the given input - output test data and the nominal linear identified model. The second part of the project is to build an efficient computer aided design software to incorporate all the above design methods. The base system of this software is MATLAB. We expect it will be a valuable tool for robust parametric control design and analysis for both theoreticians and practicing engineers.
