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Incremental passivity-based H∞ output tracking control for switched nonlinear systems

This paper is concerned with the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances using incremental passivity, even if the problem of H∞ output tracking control for none of subsystems is solvable. First, an incremental passivity concept of switched nonlinear systems without external disturbances is proposed. This incremental passivity property requires each active subsystem is incrementally passive. Then, sufficient conditions to be incrementally passive are given. Second, by resorting to the established incremental passivity theory, a state-dependent switching law and a set of feedback controllers are designed to solve the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances. This avoids solving Hamilton-Jacobi (HJ) inequality. Third, a composite state-dependent switching law and the state feedback controllers are designed to solve the H∞ output tracking problem for a class of cascaded switched nonlinear systems with external disturbances. The designed composite switching law allows the driven switched system and the driving switched system switch asynchronously. Finally, two examples are provided to verify the effectiveness of the proposed method.