Robust stabilisation of non-triangular multi-input switched non-linear systems and its application to a continuously stirred tank reactor system

The problem of global robust stabilisation is investigated for a class of multi-input switched non-linear systems where each subsystem is not assumed to be asymptotically stabilisable when applying the backstepping technique. The systems under study admit a structure which includes both the p-normal form and the nested lower triangular form as special cases. By exploiting the multiple Lyapunov functions method and the adding a power integrator technique, a sufficient condition for the solvability of the global robust stabilisation problem is derived by constructing state-feedback controllers for individual subsystems and a switching law. Also, an approach is proposed to deal with individual coordinate transformations for subsystems that are required when applying the adding a power integrator technique. The effectiveness of the proposed control scheme is illustrated by its application to a two continuously stirred tank reactor system, which cannot be handled by the existing approaches.