Persistence of excitation conditions for partially known systems

Abstmct-This note derives persistence of excitation The format of this note is the following. Section 2 stater conditions on the input for systems with partially known two excitation conditions involving both u(r) and y(t). stated transfer functions. The assumed transfer function model is i n Dasgupta n a1. (1985. 1988) and shows how they are [p,(s) + KIP(r)]/[q,,(s) + KrQ(s)]. where K is the unknown equivalent. Section 3 translates these to input-only parameter vector p,,(s). q,,(s) are known scalar polynomials conditions. Section 4 discusses cenain implications of the and P(s) and Q(s) are known vector polynomials. results in Section 3. Section 4 concludes.