H∞ controller design for switched nonlinear systems in lower triangular form under arbitrary switchings

This paper focuses on the problem of robust H_∞ control for a class of non-minimum-phase switched nonlinear systems in lower triangular form under arbitrary switchings. The backstepping design technique is applied to construct a common Lyapunov function (CLF) and an H_∞ feedback controller which guarantee that the closed-loop system is stability and the L₂-gain from the disturbance input to the controlled output is not larger than a prescribed value under arbitrary switchings. The construction of such a CLF depends on the virtual feedback controllers which are designed at each step of the iteration.