Robustness of multivariable discrete-time variable structure control

A robust stability criterion for multivariable discrete-time variable structure control is proposed. When a variable structure controller is designed and implemented as a sampled-data system, achieving robustness to uncertainties can become difficult. To ameliorate the situation, an uncertainty estimator, also formulated within the variable structure framework, can be used as an embedded discrete-time variable structure controller. This approach requires a bounded changing rate of the uncertainties to ensure robust stability. However, when uncertainties vary as a function of state variables, which occurs with parametric uncertainties, it is not practical to assume such a bound. In this paper, uncertainties are assumed to consist of external disturbances and parametric uncertainties. An uncertainty compensator is used to deal with the former, and a robust stability criterion is developed using the small gain theorem for the latter.