Stochastic controllability of linear systems with state delays.

TitleStochastic controllability of linear systems with state delays.
Publication TypeJournal Article
Year of Publication2007
AuthorsKlamka J
JournalInternational Journal of Applied Mathematics and Computer Science
AbstractIn the paper finite-dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with single point delay in the state variables are considered. Using theorem and methods taken directly from deterministic controllability problems, necessary and sufficient conditions for different kinds of stochastic relative controllability are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for controllability of linear dynamical systems with delays are also presented. Finally, minimum energy control problem for stochastic dynamical system is formulated and solved.