Sliding Modes, ∆-modulators, and Generalized Proportional Integral Control of Linear Systems

In this article, we attempt a reapproachment between sliding mode control of linear systems and classical control through the possibilities of evading state measurements and circumventing the use of asymptotic state observers in the sliding surface synthesis. This is shown to be possible thanks to the use of integral state reconstructors combined with iterated integral output error compensation. The proposed scheme is also robust with respect to unmatched perturbation inputs. A connection between sliding modes and classical analog ∆-modulators, and their natural generalization, is also brought to attention as a tool for the realization of integral reconstructor based sliding mode control schemes.