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The sensitivity of coupled continuous-time Riccati equations is analyzed through the norm of the inverse Lyapunov-like operator. This analysis leads to bounds on the perturbation of the solution. As a byproduct some properties of coupled Lyapunov equation and results on the stability of linear systems with jumps are presented.
Lower bounds for eigenvalues and matrix lower bound of a solution to continuous-time coupled algebraic Riccati equation and discrete-time coupled algebraic Riccati equation are developed as special cases of bounds for the unified coupled algebraic Riccati equation. They include bounds for the minimal eigenvalues, the sums of the eigenvalues, the trace and the determinant.
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