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Equation (4.3) is called passive if it is dissipative with respect to the supply rate (s u_{2},y_{2})=u_{2}^{T}y_{2}).
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Note that these poles are in the lower half plane (LHP) because of the sign of in the original harmonic oscillator - it was dissipative.
This excludes Hopf bifurcations (arising at tr = 0) and it means the system is dissipative, i.e. phase-space contracting all over the phase space (trace = two-dimensional Lyapunov exponent).
A dynamical system ((X, S t))) is dissipative if it possesses a bounded absorbing set, that is, a bounded set ({mathcal {B}}subset X) such that, for any bounded set (B subset X), there exists (t_{B} geq 0) satisfying S t) B subset {mathcal {B}}, quad t geq t_{B}.
We can also provide some more examples of a dissipative q.s.o. by pointing out that if an operator is dissipative, then by rearranging its components, it preserves its dissipativity.
The method is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
It is shown under a suitable condition that an algebraically stable Runge-Kutta method is dissipative when applied to the FIDEs.
Dissipativity can be verified by using the fact that V is dissipative.
It is easy to see that the equilibrium is globally asymptotically stable, and consequently the system is dissipative.
It means, that the first term induces dynamics along the curve of constant energy while the second term is dissipative and takes the direction of steepest decrease of the total energy.
A feedback control law is constructed such that the corresponding infinitesimal generator is dissipative.
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