Dynamic systems and control : Balance point bifurcation

Balance point bifurcation
Dynamic systems and control

Authors : Jean LÉVINE, Pierre ROUCHON

Review date: May 30, 2018 | Lire en français

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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 $\bar{x}$ . The latter...

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Balance point bifurcation

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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 York (1965).
(3)...

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Balance point bifurcation Dynamic systems and control

7. Balance point bifurcation

7.1 Central dynamics

Bibliography

File references

Balance point bifurcation
Dynamic systems and control