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The characterization of the solution set for a class of algebraic Riccatiinequalities is studied. This class arises in the passivity analysis of lineartime invariant control systems. Eigenvalue perturbation theory for theHamiltonian matrix associated with the Riccati inequality is used to analyzethe extremal points of the solution set.

Eigenstructure perturbations for a class of Hamiltonian matrices and solutions of related Riccati inequalities