Parameter perturbation and design of robust controllers for linear systems

摘要

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 I>stability margins in the parameter space in generall{sup}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 onthis 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 robustcontroller design problem. It can he used to synthesize robust controllers with general rational transfer functions for plants modelled as the ratio of two uncertain polynomials subjected to l{sup}p parameter perturbation.