. Sliding Mode Control in Engineering


On this basis, discontinuous feedback control strategies appeared in the

middle of the 20th century under the name of theory of variable-structure

systems. Within this viewpoint, the control inputs typically take values

from a discrete set, such as the extreme limits of a relay, or from a limited

collection of prespecified feedback control functions. The switching logic is

designed in such a way that a contracting property dominates the closedloop

dynamics of the system thus leading to a stabilization on a switching

manifold, which induces desirable trajectories. Based on these principles,

one of the most popular techniques was created, developed since the 1950s

and popularized by the seminal paper by Utkin (see [30] in chapter 7): the

sliding mode control. The essential feature of this technique is the choice

of a switching surface of the state space according to the desired dynamical

specifications of the closed-loop system. The switching logic, and thus the

control law, are designed so that the state trajectories reach the surface

and remain on it.



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