Stabilisation and H∞ control of a class of nonlinear Hamiltonian descriptor systems with application to non-linear descriptor systems

This study investigates the stabilisation and H_∞ control of a class of non-linear Hamiltonian descriptor systems (NHDSs) with application to non-linear descriptor systems (NDSs). Based on the structural characteristic of the NHDS, an equivalent non-linear Hamiltonian differential-algebraic system is obtained, and then the equivalent system is transformed into a strictly dissipative Hamiltonian form by a suitable state feedback. With the dissipative form, a stabilisation control law is developed, based on which an H_∞ controller is designed for the NHDSs with external disturbances. Finally, the obtained results for the Hamiltonian descriptor system are applied to NDSs, and a sufficient condition under which the systems can be transformed into a strictly dissipative Hamiltonian form is given. Simulation results show the efficiency of the controllers proposed in this study.