Non-Uniform in Time State Estimation of Dynamical Systems

Abstract In this paper it is showed that if a time-varying system is completely detectable then there exists an estimator for this system. Moreover, if a time-varying system is completely observable then there exists an estimator for this system that guarantees convergence of the estimates with “arbitrarily fast” rate of convergence. Finally, it is proved that under the assumption of Lipschitz complete observability, there is a global solution of the observer problem for a time-varying system.

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