Backstepping H∞ control for switched nonlinear systems under arbitrary switchings

This paper is concerned with the global H_∞ control problem for a class of switched nonlinear systems in lower triangular form under arbitrary switchings. A common Lyapunov function and a common smooth state feedback controller are constructed by backstepping such that the closed-loop system is globally asymptotically stable under arbitrary switchings without disturbance input and has the prescribed L₂-gain from the disturbance input to the controlled output. The construction of the common virtual controller during the process of backstepping relies on the domination of nonlinearity rather than the cancellation of nonlinearity. A formula is also derived to construct such a common virtual controller. Lastly, an example shows the effectiveness of the proposed method.