Abstract
For a given plant transfer function P(s) and cone size k, solutions to versions of the absolute stability problem boil down to finding a SPR multiplier Z(s) such that [k¯-1+P(s)]Z(s) is SPR. In this paper, we consider an interval plant P(s, q, r) and prove that first order multiplierslead to vertex results when establishing the positive realnells of [k¯-1+P(s,q,r)]Z(s). Additionally, we give an example of a second order multiplier and interval plant which fails to have this vertex property. These new results are then applied to the problem of robust stability of time-varying interval systems.
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