A module theoretic approach to sliding mode control in linear systems

Module theory is shown to generalize the traditional results of sliding mode control of linear systems, while introducing new possibilities for applications. The algebraic approach clearly shows that any desirable output dynamics, of arbitrary order, is synthesizable by minimum phase sliding mode control, independently of the order of the given plant and of any structural conditions of the matching type. Clear relations are also established with invertibility, nonminimum phase situations, controllability and observability