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Keywords:
linear time-invariant MIMO system; robust stability; single input single output input-output channels; MIMO uncertainty; ${\cal H}_\infty $-norm
linear time-invariant MIMO system; robust stability; single input single output input-output channels; MIMO uncertainty; ${\cal H}_\infty $-norm
Summary:
An upper bound for the complex structured singular value related to a linear time-invariant system over all frequencies is given. It is in the form of the spectral radius of the ${\cal H}_\infty $-norm matrix of SISO input-output channels of the system when uncertainty blocks are SISO. In the case of MIMO uncertainty blocks the upper bound is the $\infty $-norm of a special non-negative matrix derived from ${\cal H}_\infty $-norms of SISO channels of the system. The upper bound is fit into the inequality relation between the results of $\mu $ and $\ell _1$ robustness tests.
References:
[1] Dahleh M. A., Khammash M.: Controller design for plants with structured uncertainty. Automatica 29 (1993), 37–56 DOI 10.1016/0005-1098(93)90173-Q | MR 1200540 | Zbl 0772.93028
[2] Dahleh M. A., Diaz–Bobillo I. J.: Control of Uncertain Systems. A Linear Programming Approach. Prentice Hall, NJ 1995 Zbl 0838.93007
[3] Doyle J. C.: Structured uncertainty in control system design. In: Proc. of 24th Conference on Decision and Control, Ft. Lauderdale FL 1985, pp. 260–265
[4] Fiedler M.: Special Matrices and Their Application in Numerical Mathematics. SNTL – Nakladatelství technické literatury, Prague 1981 Zbl 0531.65008
[5] Khammash M. H., Pearson J. B.: Performance robustness of discrete–time systems with structured uncertainty. IEEE Trans. Automat. Control 36 (1991), 398–412 DOI 10.1109/9.75099 | MR 1097093 | Zbl 0754.93063
[6] Khammash M. H., Pearson J. B.: Analysis and design for robust performance with structured uncertainty. Systems Control Lett. 20 (1993), 179–187 DOI 10.1016/0167-6911(93)90059-F | MR 1208518 | Zbl 0768.93065
[7] Khammash M. H.: Necessary and sufficient conditions for the robustness of time–varying systems with applications to sampled–data systems. IEEE Trans. Automat. Control 38 (1993), 49–57 DOI 10.1109/9.186311 | MR 1201494 | Zbl 0777.93018
[8] Packard A., Doyle J. C.: The complex structured singular value. Automatica 29 (1993), 71–109 DOI 10.1016/0005-1098(93)90175-S | MR 1200542 | Zbl 0772.93023
[9] Tits A. L., Fan M. K. H.: On the small–$\mu $ theorem. Automatica 31 (1995), 1199–1201 DOI 10.1016/0005-1098(95)00035-U | MR 1342128 | Zbl 0831.93021
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