Input-Output Finite-Time Stability of Nonlinear Descriptor Systems via Hamiltonian Function Method

The problem of the input-output finite-time stability (IO-FTS) of nonlinear Hamiltonian systems is tackled in this paper. Two types of disturbance inputs, which belong to
$L_{2}$
and
$L_{\infty}$
are considered. This paper presents the sufficient condition on the basis of a dissipative Hamiltonian differential-algebraic system to study its stability with
$L_{2}$
and
$L_{\infty}$
disturbance inputs. At last, an example of a nonlinear Hamiltonian system is given, and the performance of the simulation illustrates the effectiveness of studying the IO-FTS problem via the Hamiltonian function method.