Design of MIMO integral variable structure controllers

The MIMO integral variable structure control (MIMOIVSC) scheme is proposed for a class of linear MIMO dynamic systems with nonlinear matched perturbations. This scheme is composed of two types of controllers. One is variable structure controller, which gives robust stability for system in the presence of parameter variations, uncertainties, and/or disturbances. The other is integral controller, which can eliminate steady-state error for step tracking. When the system is in the sliding mode, the dynamic equations of the closed-loop system can be reduced to a linear form and its eigenvalues can be arbitrarily assigned. In addition, an observer can be employed for state estimation, so that the state variables need not be measured. The fulfillment of sliding condition, including the case when estimated states are used, is verified. Two numerical examples are given to demonstrate the applicability of the proposed control scheme.