<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamic system. As a special case, relative stochastic controllability of dynamic systems with a single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamic systems are also presented.</p></abstract>

Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamic system. As a special case, relative stochastic controllability of dynamic systems with a single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamic systems are also presented.

Stochastic Controllability of Systems with Multiple Delays in Control

Institute of Control Engineering, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

International Journal of Applied Mathematics and Computer Science

{"article-title":"Stochastic Controllability of Systems with Multiple Delays in Control"}

Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in...

Stochastic Controllability of Systems with Multiple Delays in Control

Published Online: Apr 02, 2009

Page range: 39 - 48

DOI: https://doi.org/10.2478/v10006-009-0003-9

Keywords
controllability, linear control systems, stochastic control systems, delayed controls, multiple delays

This content is open access.

Stochastic Controllability of Systems with Multiple Delays in Control

Published Online: Apr 02, 2009

Page range: 39 - 48

DOI: https://doi.org/10.2478/v10006-009-0003-9

Keywordscontrollability, linear control systems, stochastic control systems, delayed controls, multiple delays

This content is open access.

Keywords
controllability, linear control systems, stochastic control systems, delayed controls, multiple delays