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Time domain solution to descriptor variable systems

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2 Author(s)
Zhibin Yan ; Center for Control Theory & Guidance Technol., Harbin Inst. of Technol., China ; Guangren Duan

The time domain solution to the fast subsystem of the descriptor variable system of the form Ex˙=Ax+Bu with E singular is given by Laplace inverse transformation. A new and significant feature of the solution is that it contains impulse terms excited by the values of sufficiently smooth input u and its derivatives at the initial time point. Based on the solution, the notions of consistent initial conditions, classical solutions and impulse-free solutions are discussed perfectly. The impulse controllability is discussed also which admits the same interpretation as the controllability at infinity in frequency domain.

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Automatic Control, IEEE Transactions on  (Volume:50 ,  Issue: 11 )