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Affine parameter-dependent Lyapunov functions and real parametric uncertainty

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3 Author(s)
Gahinet, P. ; Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France ; Apkarian, P. ; Chilali, M.

This paper presents new tests to analyze the robust stability and/or performance of linear systems with uncertain real parameters. These tests are extensions of the notions of quadratic stability and performance where the fixed quadratic Lyapunov function is replaced by a Lyapunov function with affine dependence on the uncertain parameters. Admittedly with some conservatism, the construction of such parameter-dependent Lyapunov functions can be reduced to a linear matrix inequality (LMI) problem and hence is numerically tractable. These LMI-based tests are applicable to constant or time-varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations. They also avoid the frequency sweep needed in real-μ analysis, and numerical experiments indicate that they often compare favorably with μ analysis for time-invariant parameter uncertainty

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Automatic Control, IEEE Transactions on  (Volume:41 ,  Issue: 3 )