Constant-time loci in the phase-plane for nonlinear systems

Abstract

This paper deals with the term constant time loci (C.T.L.) in the phase-plane and shows that in piecewise linear systems, the isoclines are also the C.T.L. A relation between the slope of the phase trajectory at any point on the phase-plane and the time taken by the system to reach that point is established, assuming any one of the isoclines as the t = 0 line. As a result, in the case of piecewise linear systems, time solutions, i.e., x vs. t, can be directly determined from the phase-plane plot. An example demonstrates the efficacy of this new approach.