A comparison of Lyapunov and hyperstability approaches to adaptive control of continuous systems

This paper contains a brief survey of certain aspects of Lyapunov's stability theory and the hyperstability theory. Conditions which have to be satisfied for the two approaches to be successfully applied to adaptive observers and controllers are examined. When all the signals in the plant are uniformly bounded (as in adaptive observers and some control problems) the two approaches yield the same results. When the plant signals cannot be assumed to be uniformly bounded (as in the general control problem) neither approach works directly and special analysis is needed.