Pi-coefficient analysis of update algorithms for adaptive systems

This paper finds the appropriate pi-coefficients for a parameter estimation adaptive system and uses them to analyze the stability of two estimation algorithms. The estimation error dynamics of the system are modeled by a linear time-invariant subsystem and a nonlinear time-varying update law in a feedback loop. Then the so-called max-p problems are formulated and solved to obtain the pi-coefficients for the linear subsystem and nonlinear update low. For the investigated system, the quantitative results show that the least-squares update algorithm has larger stability range than that of the gradient algorithm, and the σ-modification scheme gives larger stability ranges for both algorithms.