Persistency of excitation criteria for linear, multivariable, time- varying systems (Q1111523)

Persistency of excitation (PE) and sufficient richness (SR) results are of inportance for convergence studies of adaptive estimation and control schemes. This paper considers both time-invariant and time-varying linear continuous-time systems for which a number of PE and SR results are proved. Specifically: (a) Conditions are derived under which the PE of the output (or state) of a time-invariant MIMO system implies the PE of the output (or state) of another time-invariant MIMO system with the same input and dynamically related to the first; a new definition of SR for vector input signals in terms of a PE condition on a basic regression vector is also given; (b) In the SISO case exact conditions under which the PE of a signal is or is not preserved through dynamical filtering are established; and (c) Conditions are presented under which the output (or state) of a linear time-varying system is PE when its input is SR. These conditions assume that the time variations of the system parameters are either sufficiently slow or integral small.