Higher order sliding: Collection of design tools

A number of controllers named sliding algorithms of the orders 2 and 3 have been developed which add new significant possibilities to variable structure system design. The regular relay algorithm is considered as a first order controller. The controllers of the orders 2 and 3 preserve the main positive properties of the regular sliding modes. At the same time they feature bounded continuous control and guarantee precise constraint fulfillment within finite time. With discrete measurements these algorithms provide for sliding precision of their order with respect to the measurement time step. Exact robust differentiator design and aircraft pitch control are demonstrated.