Finite-time stabilisation for a class of nonlinear descriptor systems

The finite-time stabilisation, finite-time H ∞ control and finite-time adaptive H ∞ control problems for a class of nonlinear descriptor systems are studied. First, under a sufficient condition for the system impulse controllable, a finite-time stabilised controller is designed by a suitable state feedback. Then, the finite-time H ∞ control and finite-time adaptive H ∞ control problems are considered for the nonlinear descriptor system with external disturbances and/or parametric perturbations, respectively. Compared with the existing results, there is no constraint for singular matrix E, therefore controllers can be designed for more nonlinear descriptor systems. Finally, an example of the nonlinear descriptor circuit system with simulations is applied to illustrate the effectiveness of the finite-time controllers obtained in this study.