Input conditions for continuous-time adaptive systems problems

The authors develop persistence-of-excitation conditions for the exponential convergence of continuous-time adaptive algorithms. Exponential convergence is important for robustness. Adaptive algorithms without such convergence can behave unacceptably in the presence of modeling inadequacies. Conditions for convergence are usually framed as spanning conditions on a regressor vector involving the output of the unknown system. In this study the authors translate these conditions into ones involving the system input only