ABSTRACT
Sliding mode control is fundamentally a consequence of discontinuous control. In the early sixties, discontinuous control (at least in its simplest form of bang-bang control) was a subject of study for mechanics and control engineers. Just recall, as an example, Hamel's work [15] in France, or Cypkin's [27] and Emelyanov's [9] in the USSR, solving in a rigorous way the
2 A.J. FOSSARD and T. FLOQUET
problem of oscillations appearing in bang-bang control systems. These first studies, more concerned with analysis and where the phenomena appeared rather as nuisances to be avoided, turned rapidly to synthesis problems in various ways. One of them was related to (time) optimal control, another to linearization and robustness. In the first case, discontinuities in the control, occurring at given times, resulted from the solution of a variational problem. In the second, which is of interest here, the use of a discontinuous control was an a priori choice. The more or less high frequency of the commutations used depended on the goal pursued (linearization), as produced by the beating spoilers used in the early sixties to control the lift of a wing, conception of corrective nonlinear networks enabling them to bypass the Bode's law limitations and, of course, generation of sliding modes. Although both approaches and objectives were at the beginning quite different, it is interesting to note that they turned out to have much in common.
