Extension to the multivariable case

In the case of multivariable (more precisely, multi-input) systems, the determination of the control is made more delicate by the existence of several switching surfaces (m ). The desired dynamic properties are now only obtained when the sliding occurs on the intersection of all these surfaces. Starting from a given set of initial conditions, there are, in theory, an infinite number of control laws that can bring the system to this intersection and keep it there. However, we can distinguish between two classes of techniques, depending on whether we choose :

• an iterative approach, reducing to a succession of single-input problems: hierarchical control policy. In this case (figure 14 a ), a sliding regime is generated on each surface S...