An LMI Approach to Stability Analysis of Coupled Parabolic Systems
Masashi Wakaiki
TL;DR
This paper presents a method for analyzing the exponential stability of coupled parabolic PDE systems with spatially varying coefficients using LMIs and Lyapunov functions, accounting for approximation errors.
Contribution
It introduces a novel LMI-based approach that incorporates approximation errors in stability analysis of coupled parabolic systems with spatially varying coefficients.
Findings
Derived sufficient LMI conditions for exponential stability.
Accounted for approximation errors in the stability analysis.
Provided a systematic framework for stability verification of complex PDE systems.
Abstract
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis. Using a quadratic Lyapunov function, we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities.
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