Prescribed-time generalised incremental passivity of switched nonlinear systems and its application to output tracking

This paper investigates the prescribed-time generalised incremental passivity and its application to the prescribed-time output tracking control for switched nonlinear systems with multiple equilibrium or no equilibrium. First, for switched nonlinear systems, the prescribed-time generalised incremental passivity is defined. This definition permits the energy of subsystem increase during the active time interval, while at least one subsystem must be prescribed-time generalised incrementally passive on its active time interval. The energy variation of inactive subsystems is regarded as the conversion of ‘energy’ from active subsystem. Second, a state-dependent switching law with dwell time is provided for preventing Zeno behaviour from happening. Third, the prescribed-time generalised incremental passivity is used to achieve the prescribed time output tracking, even when the prescribed time output tracking for each subsystem is unsolvable. Finally, it is applied to switched pendulum system to demonstrate the effectiveness of these results.