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A note on the Lyapunov equation for discrete linear systems in Hilbert space |
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| Authors: | C. S. Kubrusly |
| Affiliation: | National Laboratory for Scientific Computation, 22290, Brazil Catholic University, Rio de Janeiro 22453, Brazil |
| Abstract: | It is given a simple and unified new proof for the following well-known stability condition: an infinite-dimensional time-invariant discrete linear system is uniformly asymptotically stable if and only if the associate Lyapunov equation has a unique strictly positive solution. The proof is partially based on an application of Rota's model construction technique. |
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