Stabilizability analysis of sphere plants

Abstract

Let p(s, δ) be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the euclidean norm constraint ‖δ‖<δ. The concept of stabilizability radius of P(s, δ) is introduced which is the norm bound δ_s for δ such that every member plant of P(s, δ) is stabilizable if and only if ‖δ‖<δ_s. The stabilizability radius can be simply interpreted as the ‘largest sphere’ around the nominal plant P(s, 0) such that P(s, δ) is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.

Keywords

real parameter uncertainty / sphere plant family / stabilizability / stabilizability radius

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