Necessary and sufficient regressor conditions for the global asymptotic stability of recursive least squares

In recursive least squares (RLS), a persistently exciting (PE) regressor guarantees global asymptotic stability (GAS) of the estimation error relative to zero equilibrium, and hence convergence parameter estimates their true values. It is known, however, that PE sufficient but not necessary for GAS, thus GAS might be achieved even if PE. Since analyses based on are ubiquitous in literature, existence non-PE regressors ensure raises question how can directly generalized into condition RLS, whether or such generalization would provide simple characterization which RLS GAS. this paper, we introduce WPE, direct explain it understood as “non-uniform” extension specific classes summation windows lower bound sequences. Next, show WPE equivalent emerges from extending certain proofs non-negative series divergence, Oresme’s divergence proof harmonic series, sequences real symmetric positive-semidefinite matrices.