Robustness enhancement of robust controller for parametrically uncertain system

The design problem of a control system is the ability to synthesize a controller that achieves robust stability and robust performance. The paper explains the finite inclusions theorem (FIT) and the FIT synthesis procedure. It is developed for synthesizing robustly stabilizing controllers for parametrically uncertain systems. 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 are Hurwitz i.e., all their roots lie in the open left-half plane. FIT 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 controllers of a 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 for solving (finite or infinite) systems of convex inequalities in an arbitrary Hilbert space. Results from examples show that the controller synthesized by FIT synthesis is better than by H_∞ synthesis with parametrically uncertain systems and satisfies the objectives for a considerably larger range of uncertainty