Stability of a class of interconnected evolution systems

Stability conditions for a class of interconnected systems modeled by linear abstract evolution equations and a memoryless nonlinearity are derived. These conditions are stated in terms of the passivity of each of the subsystems and can be considered as a partial generalization of the hyperstability theorem. A Lyapunov function approach is used in the proof without requiring the positive definiteness of the Lyapunov function. Application to the robustness analysis of the infinite-dimensional linear quadratic regulator is also discussed.<
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