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Persistency of excitation for continuous-time systems. Time-domain approach. (English) Zbl 0619.93060

This paper gives the definitions of persistently spanning (PS) with persistency interval T with respect to a vector X(t), which is a piecewise-continuous time function \(R^+\to R^ m\), and persistently exciting (PE) with richness m and persistency interval T for a piecewise- continuous scalar signal \(\xi\) (t). The continuous-time system \(y(t)=B(D)/A(D)u(t)\) can be rewritten as \(v(t)=X(t)^ T\theta\), where \(v(t)=D^ ny(t)\), \(X(t)=[D^{n-1}y(t),...,y(t),D^{n- 1}u(t),...,u(t)]^ T\), \(\theta =[-a_ 1,-a_ 2,...,-a_ n,b_ 1,...,b_ n]^ T\). Based on the definitions, the paper proves the following result for open-loop systems: If the input u is PE with richness 2n and persistency interval T, then the vector X is PS with the same persistency interval T. A similar result for closed-loop systems is also given.
Reviewer: Y.Zhang

MSC:

93E10 Estimation and detection in stochastic control theory
62F12 Asymptotic properties of parametric estimators
93B55 Pole and zero placement problems
93C40 Adaptive control/observation systems
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References:

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