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Uniform and approximative observability of nonstationary linear systems. (English. Russian original) Zbl 1079.93506

Autom. Remote Control 59, No. 7, Part 1, 907-915 (1998); translation from Avtom. Telemekh. 1998, No. 7, 3-13 (1998).
Summary: Consideration is given to the notion of uniform observability of nonstationary linear systems of ordinary differential equations, which allows one to determine at any time \(t\) the state of the system \(x(t)\) from the current values of the output and its derivatives. The necessary and sufficient conditions for uniform observability have been obtained, and classes of uniformly observed systems that are equivalent relative to a group of linear transformations have been described. Uniform observability has been shown to be equivalent to approximative observability, that is, the possibility of estimating with arbitrary precision by means of \(\delta\)-sequences the current system state without differentiating the output function.

MSC:

93B07 Observability
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations