On the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties
The problem of designing a variable structure control law for uncertain systems, where the uncertainty does not satisfy the matching conditions, is studied. A necessary and sufficient condition for the existence of a linear sliding surface in terms of linear matrix inequalities (LMI) is proved. Moreover, existence condition of a sliding surface, guaranteeing general LMI regional pole placement constraints for all admissible uncertainties, is obtained. Simulation results for controlling an inverted pendulum mounted on a cart are also presented.
scientific article; zbMATH DE number 1356092