NDLI: Efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems

Content Provider	IEEE Xplore Digital Library
Author	Balakrishnan, V. Wang, F.
Copyright Year	1998
Description	Author affiliation: Sch. of Electr. & Comput. Eng., Purdue Univ., West Lafayette, IN, USA (Balakrishnan, V.)
Abstract	Sufficient conditions for the robust stability of uncertain systems, with several different assumptions on the structure and nature of the uncertainties, can be derived in a unified manner in the framework of integral quadratic constraints. These sufficient conditions, in turn, can be used to derive lower bounds on the robust stability margin for such systems. The lower bounds are typically computed with a bisection scheme, with each iteration requiring the solution of a linear matrix inequality feasibility problem. We show how this bisection can be avoided altogether by reformulating the lower bound computation problems as generalized eigenvalue minimization problems, which can be solved very efficiently using standard algorithms. Our approach can be applied to many important, commonly-encountered special cases: diagonal, nonlinear uncertainties; diagonal, memoryless, time-invariant sector-bounded ("Popov") uncertainties; structured dynamic uncertainties; and structured parametric uncertainties. We also illustrate, using a numerical example, the computational savings that can be obtained with our approach.
Starting Page	4406
Ending Page	4407
File Size	225982
Page Count	2
File Format	PDF
ISBN	0780343948
ISSN	01912216
DOI	10.1109/CDC.1998.762006
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1998-12-18
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Robust stability Uncertainty Eigenvalues and eigenfunctions Uncertain systems Sufficient conditions Terminology Integral equations Linear matrix inequalities Minimization methods Linear systems
Content Type	Text
Resource Type	Article

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