What question did this study set out to answer?

To develop computationally tractable robust stability and performance tests for linear systems subject to real parametric uncertainty using affine parameter-dependent Lyapunov functions.

March 1, 1996IEEE Transactions on Automatic Control

Affine parameter-dependent Lyapunov functions and real parametric uncertainty

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Authors

PGP. GahinetApple (United States)PAPierre ApkarianSystem Dynamics International (United States)MCM. ChilaliInstitut national de recherche en sciences et technologies du numérique

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Implication

Theoretical study demonstrates enhanced robust stability testing in uncertain linear systems, suggesting lower conservatism than quadratic stability.

Key Points

To develop computationally tractable robust stability and performance tests for linear systems subject to real parametric uncertainty using affine parameter-dependent Lyapunov functions.
Extended conventional quadratic stability and performance formulations by introducing Lyapunov functions that depend affinely on uncertain parameters.
Cast the construction of parameter-dependent Lyapunov functions as a solvable linear matrix inequality (LMI) optimization problem for constant and time-varying parameters.
Demonstrated that the LMI-based tests exhibit less conservatism than standard quadratic stability when evaluating systems with slow parametric variations.
Eliminated the need for frequency sweeps required by real-mu analysis, with numerical simulations indicating favorable performance compared to mu analysis for time-invariant uncertainty.

Cite This Study

Gahinet et al. (1996) studied this question.

synapsesocial.com/papers/69ffce6b4716aad0cc8579cc https://doi.org/10.1109/9.486646

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Implication

Theoretical study demonstrates enhanced robust stability testing in uncertain linear systems, suggesting lower conservatism than quadratic stability.

Affine parameter-dependent Lyapunov functions and real parametric uncertainty

Discussion

Member takes

Implication

Key Points

Cite This Study

Affine parameter-dependent Lyapunov functions and real parametric uncertainty

Discussion

Member takes

Implication

Key Points

Cite This Study

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