Qualitative dynamics, root-loci and asymptotic structure of universal adaptive stabilizers

A problem of universal adaptive stabilization in Rⁿ is approachedin a qualitative manner to relate the form of the trajectoriesin the extended state space Rⁿ⁺¹ to the root locus of the associatedfixed-parameter linear system. Relationships are derived betweenthe values of the limit gain and the initial conditions. Numericalstudies are used to illustrate and support these ideas by computationof generic trajectories and attempted computation of certainnon-generic possibilities. The implications of the study formore general dynamic situations are outlined. These authors are also with the Department of Mathematics,University of Exeter, EX4 4QE.