Design of Robust Strictly Positive Real Transfer Functions

Abstract

This chapter studies the robust synthesis problem for strictly positive real (SPR) transfer functions. The concepts of SPR regions and weak SPR regions are introduced. By using the complete discrimination system (CDS) for polynomials, complete characterization of the (weak) SPR regions for transfer functions in coefficient space is given. It is shown that the weak monic SPR region associated with a fixed polynomial is bounded and the intersection of several weak monic SPR regions associated with different polynomials cannot be a single point. Furthermore, we show how to construct a point in the SPR region from a point in the weak SPR region. Based on these theoretical development, we propose an algorithm for robust design of SPR transfer functions. This algorithm works well for both low-order and high-order polynomial families. Especially, the derived conditions are necessary and sufficient for robust SPR design of polynomial segment or low-order (n ≤ 4) interval polynomials. Illustrative examples are provided to show the effectiveness of this algorithm.