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A decoupled approach to filter design for stochastic systems. (English) Zbl 1353.93112

Summary: This paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems. This result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept. Two kinds of observers are treated: the full-order and reduced-order cases.

MSC:

93E11 Filtering in stochastic control theory
93E10 Estimation and detection in stochastic control theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93C10 Nonlinear systems in control theory
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