Eigenvalue assignment for the sliding hyperplane

The central feature of variable structure control (VSC) is that the nonlinear feedback control is discontinuous on the switching surfaces of the state space. The main property of a VSC system is its invariance to a class of matched parameter variations and disturbances. This results in a robust control system without the need for precise determination of parameter values. A suitable control function is determined to ensure the attainment of the sliding manifold and the existence of the sliding mode. The paper concerns the design of the sliding hyperplanes which specify the dynamic behaviour of the system in the sliding mode by assigning eigenvalues in a specified region. Three approaches are described and are tested on a multivariable system. The methods differ in the region to which the eigenvalues are assigned; in one case it is a disc, in another a vertical strip, and in the third a symmetrical cone