Variable structure control systems: Synthesis of scalar and vector systems by state and output feedback

Modern views are applied to examine synthesis of variable structure systems (VSS) for SISO and MIMO systems of general position in the presence of information on the full phase vector or only on the output vector. In the latter case we consider separately the cases of organizing a sliding mode in plant output coordinates and in arbitrary coordinates. The latter case requires the construction of asymptotic observers for linear systems with uncertainty in the parameters or in inputs, and the corresponding observation theory is sketched. Special attention is given to the case of so-called hyperoutput systems, i. e., multiply connected systems in which the number of outputs exceeds the number of inputs. For hyperoutput systems under fairly general conditions we can arbitrarily choose the observer dynamics, which is important for improving the performance of the control system as a whole. We show that the observer dynamics does not change the VSS stability. © 2010 Springer Science+Business Media, Inc.