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Lower bounds on the solution of coupled algebraic Riccati equation. (English) Zbl 0990.93043
Lower bounds for eigenvalues and lower matrix bounds of the solution to a continuous-time coupled algebraic Riccati equation (CCARE) and a discrete-time coupled algebraic Riccati equation (DCARE) are developed. These bounds are obtained 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. Two low-order numerical examples are presented. The examples suggest that the bounds for CCARE can be very conservative, the bounds for DCARE being quite satisfactory.
MSC:
93B60Eigenvalue problems in systems theory
49N10Linear-quadratic optimal control problems
15A24Matrix equations and identities
15A45Miscellaneous inequalities involving matrices
15A15Determinants, permanents, other special matrix functions