On discrete variable structure control with switching sector

In this chapter, potential instability and performance limitation due to the use of an attractive and non-invariant switching sector in a number of discrete variable structure controllers (DVSCs) for linear systems with parametric uncertainties are discussed. Analytical explanation as well as counter examples are given to support the arguments. A state feedback DVSC based on the concept of switching sector and capable of avoiding the potential pitfalls is proposed. It is shown that global uniform asymptotic stability can be achieved despite the non-attractiveness and non-invariance of the switching sector. Conservativeness of the proposed controller is investigated and a numerical example is presented.