Stability analysis and feedback design of a direct current–direct current power converter by vector Lyapunov function

Abstract

SummaryTo prove the stability of hybrid systems, where, several subsystems are in series–parallel arrangement, Vector Lyapunov functions are appropriate substitutes for the scalar Lyapunov ones. By assigning a scalar Lyapunov function to each subsystem, the stability of the whole hybrid system can be analyzed. In this paper, having reviewed the preliminaries, a direct current (DC) –DC converter working as an incremental voltage source is selected. We show that the conditions of the vector Lyapunov stability are satisfied by deriving the variation interval for the feedback coefficients and obtaining the appropriate feedback factor given the desired output. Simplicity and less restrictedness of vector Lyapunov method is shown comparatively. All the derived mathematical relations are validated by numerical computations.