Robustness of discrete-time variable structure control to parametric uncertainties and exogenous disturbances

A robust stability condition for discrete-time variable structure control is proposed. Conventionally the discrete-time variable structure control method with a variable structure uncertainty estimator approach requires a bounded changing rate of the uncertainties to ensure robust stability. However, when uncertainties vary as a function of state variables, which occur with parametric uncertainties, it is not practical to assume a bounded rate on the uncertainties. In the paper, uncertainties are assumed to consist of exogenous disturbances and parametric uncertainties. An uncertainty compensator is used to deal with the former, and a robust stability condition is derived using small gain theorem for the latter