It is shown that testing a matrix A /spl isin/ R/sup nxn/ for discrete-time D-stability is equivalent to testing if the structured singular value (SSV or /spl mu/) of a matrix M /spl isin/ R/sup 2nx2n/ obtained from A, is less than unity. Testing for D-semistability (i.e. the property that the product AD has all eigenvalues in the closed left half plane) is shown to be equivalent to testing if the SSV of (M-I)/sup -1/(M+I) is less than or equal to unity. The existence of the Fan-Tits-Doyle LMI-based upper bound for CL (1991) is shown to imply the existence of a diagonal solution to the discrete-time Lyapunov equation in A.
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