Integral sliding mode in systems operating under uncertainty conditions

The paper generalized a new sliding mode design concept, namely integral sliding mode (ISM). The order of the motion equation in ISM is equal to the order of the original system, rather than reduced by the number of dimension of the control input. As the result, robustness of the system can be guaranteed throughout an entire response of the system starting from the initial time instance. Uniform formulations of the ISM design principle are developed in the paper. It is shown through examples that our generalized ISM scheme enables a wide scope of application areas. In the case that the given control matrix can not be used directly for generating the sliding mode, the associated decoupling problem was also discussed based on the concept of sliding mode transformation. To alleviate chattering, we remove the discontinuous control action from the real control path and insert it to an internal dynamic process for generating the sliding mode