Abstract
The guardian map theory of generalized stability of parametrized linear time-invariant systems is used to prove new results on stability/performance of linear time-invariant singularly perturbed systems with an exogenous parameter, i.e. systems that contain, in addition to a singular parameter ϵ, another uncertain parameter μ. The results give necessary and sufficient conditions for generalized stability for all sufficiently small values of ϵ and all values of μ in a given interval [ μ 1, μ 2]. In addition, explicit expressions for the largest upper bound ϵ ∗ on ϵ for guaranteed stability and performance are given and the cases leading to finite or infinite ϵ ∗ are clearly delineated. Thus the results represent a significant addition to the classical Klimushev-Krasovskii theorem, while at the same time providing closed-form expressions for the maximum parameter range for stability and performance.
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