lp parameter perturbation and design of robust controllers for linear systems

In this paper, linear systems with characteristic equations that are linearly dependent on some uncertain parameters are considered. A new procedure is proposed for the calculation of D-stability margins in the parameter space in general l(P)-norms. The procedure is simple and computationally efficient. For several important regions of interest in the complex plane, e.g. left hand plane, sectors and circles centred at the origin, it requires the solution of only one equation. Based on this result, a new method is presented for the design of robust controllers. Robust placement of the closed-loop poles inside the regions of interest is addressed. The method provides a simple and computationally tractable solution to the robust controller design problem. It can be used to synthesize robust controllers with general rational transfer functions for plants modelled as the ratio of two uncertain polynomials subjected to l(P) parameter perturbation.