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On the bounds on the solutions of the algebraic Lyapunov and Riccati equations

Czornik A., Nawrat A.

Archives of Control Sciences

2000

Vol. 10, no. 3/4

197-244

Different types of bounds for solutions of continuous and discrete Lyapunov and Riccati equations obtained up to now are summarized in this paper. Some new bounds are also presented. The efficiency of each bound is illustrated with three numerical examples. A discussion and comparison are given as well. The results may be particularly convenient to get the ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds.