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Lyapunov function of a fourth-order system

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1 Author(s)
Ku, Y. ; Uni. of Pennsylvania, Philadelphia, PA, USA

The Lyapunov functionVand its time derivativedot{V}are expressed in matrix form byx'Sxandx'Tx, respectively, whereSandTcontain elements which involve the state variables, andx'is the transpose ofx. A given fourth-order nonlinear system is characterized bydot{x}=A(x)x, whereA(x)contains nonlinear elements. Simanov's problem is extended to a fourth-order system whose nonlinearity is a constrained function of two state variables.

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Automatic Control, IEEE Transactions on  (Volume:9 ,  Issue: 3 )