A new switching function for variable structure control

A new switching function for variable structure control is proposed in this paper for linear continuous-time systems with uncertainties. It consists of an ordinary linear term plus an integral term and allows direct use of the pole placement technique. Different design methods are used for systems with matched and mismatched uncertainties. For systems with matched uncertainties, the switching function is synthesised based on the Riccati equation. For systems with mismatched uncertainties, the switching function is designed using the technique of linear matrix inequality. Variable structure controllers are developed according to the reaching condition of the sliding mode. Furthermore, the results for continuous-time systems are extended to discrete-time systems. The proposed approach is illustrated through numerical simulations.