Optimal filtering for a class of linear Itô stochastic systems: the dichotomic case. (English) Zbl 1387.93160
Summary: This paper focuses on the problem of optimal \(\mathcal{H}_2\) filtering for a class of continuous-time stochastic systems without assuming their exponential stability in the mean square sense. Indeed, the stability assumption is relaxed and we assume instead that the Lyapunov operator associated to the dynamical stochastic system is exponentially dichotomic. The optimal solution of the considered optimization problem is expressed in terms of the unique solution of a suitable algebraic Lyapunov equation and the stabilizing solution of a certain algebraic Riccati equation.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93E10 | Estimation and detection in stochastic control theory |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
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