アブストラクト
| Date | 11:00-12:00 Nov 28, 2023 |
| Speaker | Graziano Chesi Professor, Department of Electrical and Electronic Engineering, The University of Hong Kong |
| Title | Exact LMI Conditions for Stability and L2 Gain Analysis of 2D Systems via Quadratically-Frequency-Dependent Lyapunov Functions |
| Abstract |
This talk presents our recent results about the problems of establishing
stability and performance of 2D systems. The first result states that
Lyapunov functions quadratically dependent on the frequency are exact
for establishing stability. This is particularly important since the
existing works that exploit Lyapunov functions provide a much larger
upper bound on the dependence on the frequency or other parameters. The
second result provides a novel linear matrix inequality (LMI) necessary
and sufficient condition for establishing the existence of such Lyapunov
functions. It is shown, analytically and through several examples, for
both best and worst cases, that the numerical complexity of this novel
condition is significantly smaller than that of the existing methods.
The third result explains how the proposed methodology can be used to
establish upper bounds on the L2 gain, in particular, deriving a novel
necessary and sufficient LMI condition based on Lyapunov functions
quadratically dependent on the frequency.
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