Robust Controller Design for Parametrically Uncertain System

The design problem of the control system is the ability to synthesize controller that achieve robust stability and robust performance. The paper explains the Finite Inclusions Theorem (FIT) by the procedure namely FIT synthesis. It is developed for synthesizing robustly stabilizing controller for parametrically uncertain system. The fundamental problem in the study of parametrically uncertain system is to determine whether or not all the polynomials in a given family of characteristic polynomials is Hurwitz i.e., all their roots lie in the open left-half plane. By FIT it can prove a polynomial is Hurwitz from only approximate knowledge of the polynomial's phase at finitely many points along the imaginary axis. An example shows the simplicity of using the FIT synthesis to directly search for robust controller of parametrically uncertain system by way of solving a sequence of systems of linear inequalities. The systems of inequalities are solved via the projection method which is an elegantly simple technique fur solving (finite or infinite) systems of convex inequalities in an arbitrary Hilbert space. Results from example show that the controller synthesized by FIT synthesis is better than by H$\sub$$\infty$/ synthesis with parametrically uncertain system as well as satisfied the objectives for a considerably larger range of uncertainty.