Equilibrium Point(Examples). Ex:. Find equilibrium point. (i). This implies that. (ii). Analyze the stability of the equilibrium point. (i). Equilibrium Point(Examples). (ii). Thus the system is (globally) asymptotically stable. Instability Theorem. Instability Theorem.
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Find equilibrium point.
This implies that
Analyze the stability of the equilibrium point.
Thus the system is (globally) asymptotically stable.
If these conditions are met, the following can be constructed
continuously differentiable p.d.
Using the idea of limit set & invariant set, it can be proved.
minors are all
Proof : Sufficiency follows from the Lyapunov stability theorem.