Vu Ngoc Phat, Tran Tin Kiet, "On the Lyapunov equation in Banach spaces and applications to control problems", International Journal of Mathematics and Mathematical Sciences, vol. 29, Article ID 419587, 12 pages, 2002. https://doi.org/10.1155/S0161171202010840
On the Lyapunov equation in Banach spaces and applications to control problems
By extending the Lyapunov equation to an arbitrary infinite-dimensional Banach space, we give stability conditions for a class of linear differential systems. Relationship between stabilizability and exact null-controllability is established. The result is applied to obtain new sufficient conditions for the stabilizability of a class of nonlinear control systems in Banach spaces.
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