Controller design improving robustness properties for parametrically uncertain system

The design problem of the control system is the ability to synthesize a controller that achieves robust stability and robust performance. The paper explains the finite inclusions theorem (FIT) by the procedure namely FIT synthesis. It is developed for synthesizing a robustly stabilizing controller for parametrically uncertain systems. The fundamental problem in the study of parametrically uncertain systems 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. By using the FIT it can be proved that a polynomial is Hurwitz from only approximate knowledge of the location of a finite number of polynomial value sets at appropriately chosen frequencies. 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. We design a stabilizing controller for the nominal plant. Once an initial controller is found, the algorithm iteratively improves on the controller until the desired specifications are met. Results from an example show that the controller synthesized by FIT synthesis is better than by H_∞ synthesis with parametrically uncertain system