Lower bounds on the solution of coupled algebraic Riccati equation. (English) Zbl 0990.93043

Czornik, Adam; Swierniak, Andrzej

Automatica 37, No. 4, 619-624 (2001).

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.

Reviewer: Petko Hr.Petkov (Sofia)

MSC:

93B60	Eigenvalue problems
49N10	Linear-quadratic optimal control problems
15A24	Matrix equations and identities
15A45	Miscellaneous inequalities involving matrices
15A15	Determinants, permanents, traces, other special matrix functions

Keywords:

lower bounds for eigenvalues; lower matrix bounds; continuous-time coupled algebraic Riccati equation; discrete-time coupled algebraic Riccati equation; trace; determinant

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