Stability margins and robust controller design for multilinear systems

摘要

In this paper, linear systems with the characteristic equations that are multilinearly 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 is computationally feasible. It requires the numerical solution of a system of equations in each frequency. The Minimum Distance Approach used in previous works for polynomials with linearly-dependent coefficients is generalised in here for the case of polynomials with multilinearly-dependent coefficients. Based on the above approach for the calculation of D-stability margins, a 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 for the synthesis of robust controllers for multilinear systems.