Range-space dynamics of scalar-variable-structure control systems

The dynamic behaviour of the range space of a linear operator mt used to form a switching function in a scalar-variable-structure control system is described. It is shown that as the operator mt is defined for less than the full-state vector complement, the dynamic order of the range space increases. It is also shown that the range space can be stabilised by compensation techniques, without affecting the null space behaviour of the control system.