An integral inequality design method of robust control schemes for uncertain nonlinear systems with universal uncertainties

The problem of robust control is considered for a class of uncertain nonlinear systems with completely unmatched uncertainties. Here the system uncertainties do not satisfy any matching conditions and are only assumed to mathematically guarantee the existence of solutions to differential equations which describe some actual systems, and to not destroy the stabilisability of any uncertain systems. In this paper, such a uncertainty is called universal uncertainty. Based on an integral inequality, instead of Lyapunov function, a new design method is proposed such that some stabilising control schemes with a rather simple structure can be synthesised, for such a class of uncertain nonlinear systems with universal uncertainties. Particularly, the universal uncertainty defined in the paper can cover most unmodelled parts of actual plants, meanwhile, which implies that the results obtained in the paper can be applied to almost all of practical control systems with unknown parts. Finally, a numerical examples are given to demonstrate the simplicity of the proposed design method of robust control schemes.