A study of PD-characteristic equations for time-varying linear systems using coordinate transformations

This paper is concerned with a Riccati type class of nonlinear differential equations called parallel D-characteristic (PD-characteristic) equations, associated with time-varying linear dynamic systems which are described by differential equations. The solutions of PD-characteristic equations are known to possess singularities (finite-time escapes), which greatly hampers their use in the analysis and control of time-varying linear systems. A theorem is developed to show that the solutions of PD-characteristic equations are well-behaved near the singularities This result allows the classical notion of continuability of solutions to be extended through such singularities. A number of coordinate transformations are also discussed which facilitate numerical integration through such singularities