Article | REF: S7430 V1

Dynamic systems and control

Authors: Jean LÉVINE, Pierre ROUCHON

Publication date: September 10, 2008

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7. Balance point bifurcation

7.1 Central dynamics

When the eigenvalues of the Jacobian matrix $\frac{\partial f}{\partial x} (\bar{x}, \bar{u}, \bar{w})$ are, in part, negative real-valued with others on the imaginary axis, we can no longer draw conclusions regarding the stability of the equilibrium $\bar{x}$ ...

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Balance point bifurcation

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page Balance and stability

Lyapunov function and stabilization

Bibliography

File references

(1) - ABRAHAM (R.H.), SHAW (C.D.) - Dynamics – The Geometry of Behavior : I-IV. - Aerial Press, Santa Cruz, California (1981).
(2) - ABRAMOWITZ (M.), STEGUN (I.A.) - Handbook of Mathematical Functions. - Dover, New...

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Center Automatique et Système (CAS) at École des mines de Paris http://www.ensmp.fr

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