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Stability and bifurcation analysis of differential-difference-algebraic equations

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2 Author(s)
Luonan Chen ; Dept. of Electr. Eng. & Electron., Osaka Sangyo Univ., Daito, Japan ; Aihara, K.

This paper treats a nonlinear dynamical system with both continuous-time and 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 perturbations and bifurcations, and further shows that there exist four types 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 digital control of power systems as an example. Numerical simulations demonstrate that our results are useful

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:48 ,  Issue: 3 )