Technical Communique: Upper bounds for the solution of the discrete algebraic Lyapunov equation

Authors:
Michael K. Tippett;Dan Marchesin
Affiliations:
Centro de Previsão de Tempo e Estudos Climáticos, Cachoeira Paulista, SP, Brazil;Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro, RJ, Brazil
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Abstract

New upper bounds for the solution of the discrete algebraic Lyapunov equation (DALE) P=APA^T+Q are presented. The only restriction on their applicability is that A be stable; there are no restrictions on the singular values of A nor on the diagonalizability of A. The new bounds relate the size of P to the radius of stability of A. The upper bounds are computable when the large dimension of A make direct solution of the DALE impossible. The new bounds are shown to reflect the dependence of P on A better than previously known upper bounds.