New adaptive algorithms in Lyapunov synthesis

The speeds of the adaptive response of Lyapunov-designed adaptive systems are related to some extent to the degree of stability of the system. A generalized quadratic Lyapunov function is constructed to allow several new adaptive algorithms to be synthesized. The new algorithms each improve the degree of stability over previously reported adaptive algorithms. A root-locus analysis substantiates the improvement in response speed. While the framework for this short paper is that of full-state model-reference adaptation, the synthesis is applicable to systems employing output measurement, such as reduced-order model-reference systems [5] or an adaptive observer [20].