A functional analytic approach to infinite dimensional stochastic linear systems. (English) Zbl 1472.93177
Summary: In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [Q. Lü, ibid. 53, No. 6, 3457–3482 (2015; Zbl 1327.93358)].
Second, we propose a new variation of constants formula for mild solutions of perturbed abstract stochastic Cauchy problems using the concept of Yosida extensions of admissible operators. Third, we prove the well-posedness of perturbed boundary control systems. Fourth, we apply this result to a general class of stochastic systems with delays in state, control, and observation parts. Finally, we study admissible observation operators and exact observability for semilinear stochastic systems.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 93C35 | Multivariable systems, multidimensional control systems |
| 93C05 | Linear systems in control theory |
| 93B07 | Observability |
| 93C73 | Perturbations in control/observation systems |
Keywords:
stochastic well-posed systems; admissible operators; Yosida extensions; observability of semilinear stochastic systems; stochastic delay systemsCitations:
Zbl 1327.93358References:
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