Liapunov’s Stability Critearia
November 24, 2008 Leave a comment
The system is stable throughout the region where dV/dt is negative-semidefinite for all nonzero x and t>0
The system is asymtotically stable in the region if dV/dt is negative-definite
The system is globally asymtotically stable if dV/dt is negative-definite in the entire state space governed by the variable x
Since V > 0, V(0)=0, V is positive-definite
Since W < 0, V(0)=0, V is negative-definite
2. Linear Oscillator
Hence, the system is globally stable
Since V(0)=0, V>0, W<0,
The system is globally asymtotically stable.
Kolk, W. Richard, Lerman, Robert A., Nonlinear System Dynamics, van Nostrand Reinhold, USA, page 191,1992.