| On the Gap Between Structured Singular Values and Their Upper Bounds (2007) | |||||||||||||
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| A geometric description of the gap between complex structured singular value (SSV or ) and its "D-scaling" upper bound is given. As an application, it is shown that the gap grows not faster than linearly in the number of uncertain blocks. 1. Introduction The structured singular values (SSV or ) were introduced to study robustness of linear timeinvariant systems with structured uncertainty (see, for example, the original paper [1] and the more recent treatment in [2]). Calculating exact SSV is di#cult, so computable upper and lower bounds are used in practice. The upper bounds give su#cient conditions of robust stability /performance while a lower bound can be used to check how conservative these su#cient conditions are. In this paper we study the case of the well-known D-scaling upper bound for complex SSV. Numerical experiments show that the "gap" between SSV and its upper bound is small: the ratio is always greater than 0.8. However, no mathematical proof (or counterexample) is know... | |||||||||||||
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