A new integral inequality and its applications to robust control problems of uncertain nonlinear systems

Abstract

SummaryIn this paper, a new integral inequality is presented. By combining this integral inequality with adaptive approach, new design methods can be developed to synthesize some adaptive robust control schemes for a large class of uncertain nonlinear systems and to deal with well the unknown nonlinearities appearing in uncertain nonlinear control dynamical systems. As an application of the presented integral inequality to control theory, the robust stabilization problem is considered for a class of uncertain strict‐feedback nonlinear systems with both time‐delay and unknown dead‐zone input nonlinearities. It is shown that there are two main merits in the design method based on the integral inequality presented in this paper. The first one is that one need not estimate and know the unknown nonlinearities to synthesize some stabilizing control schemes. The second one is that the resulting feedback control schemes have rather simple structure.