Bifurcation analysis of hybrid dynamical systems

Defines a model formulated by differential-difference-algebraic equations (DDA) as a hybrid dynamical system (HDS) or constrained sampled-data model. So far, both continuous-time and discrete-time nonlinear systems have attracted considerable attention and a variety of techniques have been developed. In contrast, however, the researches for the hybrid systems are mainly for the systems defined by both differential equations with continuous states and logical-discrete-event equations with discrete states. On the other hand, the sampled-data models or differential-difference equations where all of the states are continuous are investigated mostly for the linear systems. Less attention has been focused on the nonlinear analysis of the DDA or the hybrid dynamical systems where the differential and the difference equations not only have continuous states but also are constrained by algebraic equations. As part of a continuing series of works which attempt to elucidate the properties of HDS following the analysis of the asymptotical stability in previous papers, this paper aims at analysing bifurcations of HDS and further applying the theoretical results to digital control of power systems.