Adapted solution of a backward stochastic differential equation
Systems & Control Letters
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Automatica (Journal of IFAC)
Stochastic Controllability of Linear Systems With State Delays
International Journal of Applied Mathematics and Computer Science
Brief paper: Complete controllability of impulsive stochastic integro-differential systems
Automatica (Journal of IFAC)
Input-to-state stability of impulsive and switching hybrid systems with time-delay
Automatica (Journal of IFAC)
Robust Fuzzy Design for Nonlinear Uncertain Stochastic Systems via Sliding-Mode Control
IEEE Transactions on Fuzzy Systems
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This paper is concerned with the controllability of linear impulsive stochastic systems (LISSs) in Hilbert spaces. For this class of systems, the concepts of null controllability and approximate null controllability are introduced. To overcome the difficulties related, we construct the adjoint systems and the quasi-backward stochastic systems of LISSs. Necessary and sufficient conditions for the null controllability and the approximate null controllability are developed by utilizing our introduced quasi-backward stochastic systems. Furthermore, an equivalence is established between the null controllability of LISSs and some initial state of quasi-backward stochastic systems.