Persistence of Excitation in Linear Systems

This paper develops output reachability characterizations of linear finite dimensional systems, so as to translate excitation properties of system inputs to excitation properties of system outputs, states, or associated regression vectors. Such properties are of fundamental concern for convergence of algorithms involving on-line identification, adaptive state estimation, prediction and control. The case of adaptive control is of particular interest since it is desirable that persistence of excitation of associated regression vectors be maintained in the presence of time-varying feedback controllers. Persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties. The theory of the paper suggests modifications to standard adaptive schemes to ensure the required persistence of excitation.