Stability and bifurcation analysis of differential-difference-algebraic equations

This paper treats a nonlinear dynamical system with both continuous-time an d discrete-time variables as a differential-difference-algebraic equation ( DDA) or a hybrid dynamical system, presents a fundamental analyzing method of such a DDA system for local sampling, asymptotical stability, singular p erturbations and bifurcations, and further shows that there exist four type s of generic codimension-one bifurcations at the equilibria in contrast to two types in continuous-time dynamical systems and three types in discrete- time dynamical systems. Finally the theoretical results are applied to digi tal control of power systems as an example. Numerical simulations demonstra te that our results are useful.