Linear systems with a polynomial uncertainty structure: stability margins and control

In this paper, the stability and control of linear systems with parameter uncertainty are considered. The characteristic equations of such systems are derived as functions of uncertain parameters. The cases in which the coefficients are polynomial functions of the uncertain parameters are studied and an algorithm is presented for the calculation of stability margins in the parameter space in general l(p)-norms. The stability is defined with respect to arbitrary regions in the complex plane (so-called D-stability). The algorithm requires a search on the contour of the region (frequency search) and to solve a system of equations at each step. Using the above algorithm, a method is also presented for the design of robust controllers for systems with uncertain parameters and robust pole placement inside the regions of interest is addressed.