Title :
Affine parameter-dependent Lyapunov functions for real parametric uncertainty
Author :
Gahinet, Pascal ; Apkarian, Pierre ; Chilali, M.
Author_Institution :
Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France
Abstract :
A new test of robust stability/performance is proposed for linear systems with uncertain real parameters. This test is an extension of the notion of quadratic stability 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 an linear matrix inequality (LMI) problem, hence is numerically tractable. This LMI-based test can be used for both fixed or time-varying uncertain parameters and is always less conservative than the quadratic stability test whenever the parameters cannot vary arbitrarily fast. Its also completely bypasses the frequency sweep required in real μ-analysis
Keywords :
Lyapunov methods; linear systems; matrix algebra; robust control; uncertain systems; affine parameter-dependent Lyapunov functions; linear matrix inequality; linear systems; quadratic stability; real parametric uncertainty; robust stability; time-varying uncertain parameters; Circuit stability; Circuit testing; Control systems; Frequency; Linear systems; Lyapunov method; Robust control; Robust stability; System testing; Uncertainty;
Conference_Titel :
Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on
Conference_Location :
Lake Buena Vista, FL
Print_ISBN :
0-7803-1968-0
DOI :
10.1109/CDC.1994.411442
