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We analyze the exponential stability of distributed parameter systems. Thesystem we consider is described by a coupled parabolic partial differentialequation with spatially varying coefficients. We approximate the coefficientsby splitting space domains but take into account approximation errors duringstability analysis. Using a quadratic Lyapunov function, we obtain sufficientconditions for exponential stability in terms of linear matrix inequalities.

An LMI Approach to Stability Analysis of Coupled Parabolic Systems