Affine parameter-dependent Lyapunov functions and real parametric uncertainty

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 affi...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1996-03, Vol.41 (3), p.436-442
Main Authors: Gahinet, P., Apkarian, P., Chilali, M.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Differential equations
Eigenvalues and eigenfunctions
Exact sciences and technology
Linear systems
Lyapunov method
Observability
Riccati equations
Stability
Testing
Time measurement
Uncertainty
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Summary: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-/spl mu/ analysis, and numerical experiments indicate that they often compare favorably with /spl mu/ analysis for time-invariant parameter uncertainty.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.486646