Synthesis of robust stabilizers with real coefficients by the method of Nevanlinna and Pick (Q1319733)

The problem of feedback stabilizing a whole class of linear systems defined by some reference transfer function with an additive bounded nonparametric uncertainty is addressed. Necessary and sufficient conditions for the solvability of this problem as well as an analytic characterization of the entire class of stabilizing controllers were given by Doyle (1094), Vidyasagar (1985), Glover and McFarlane (1990). Moreover, the synthesis problem of any stabilizing controller is equivalent to the interpolation problem in the class of Schur functions. Necessary and sufficient conditions for the solvability of this problem has been known since the works by Pick and Nevanlinna (1919) who proposed an iterative algorithm, starting form a generating initial function. If the reference transfer function has a pair of unstable complex poles, then Pick and Nevanlinna procedure usually synthesizes transfer functions of the robust controller with complex coefficients. In this paper, a special choice of the generating initial function is proposed which leads to robust stabilizers with real coefficients. Simulation results illustrate the proposed procedure.