EXPONENTiAL CONVERGENCE AND ROBUSTNESS OF PERSISTENTLY EXCITED RECURSIVE-LEAST-SQUARES-WITH-FORGETTING OUTPUT NROR IDENTIFICATION

tions. Thus a viewpoint is presented here that suggests a broad category of well-behaved, This note demonstrates the exponential robust identification schemes. convergence of the recursive-least-squares-withWe begin by stating the RLSF output error forgetting (RLSF) type output error identifier algorithm and manipulating it to fit a general via the exponential stability of an associated, error model Next, an exponential yet more general, error model fornulation. This stability result is presentedfor the general general error model approach encompasses several error model, together .dith a discussion of the similarly well-behaved variants of output and equation error identification schemes. A persistent excitation conditions involved. This is the key result required to show the exponential persistent excitation property imposed on plant of output RSLF. ~ i ~ ~ l l ~ , inputs alone, related to the order of the assumed plant ARMA model, is shown to provide recuced order modeling and plant time variation are shown to cause disturbance inputs to and ths robust, exponentially convewent identificachanges in the state transition matrix of the tion useful for such applications as those involving model order underestimation andlor homogeneous, exponentially stable error model plant parameter time-variation. The nonlinear, of the ideal application. Therefare identification based on the form of the general error model time-varying, forced error model associated with presented here can be snorn to possess robust RSLF output error identification is derived for behavior for suitably small disturbances by such non-ideal situations. invoking the results of [7].