Integral sliding‐mode‐based robust output‐regulation for constrained and uncertain linear systems

This article proposes a solution to the output regulation problem for uncertain linear systems with input saturation, state constraints, and external disturbances. The proposed robust control is composed of a linear and a nonlinear part. Each part of the control can be designed independently due to the use of an integral sliding‐mode control approach. The linear control, whose design is based on the barrier Lyapunov function and the attractive ellipsoid method, considers the input saturation, the state constraints, and the parameter uncertainties. The nonlinear part is based on an integral sliding‐mode control approach and it can compensate the effect of some matched disturbances. Also, a safe set where the system trajectories do not transgress the state constraints and input saturation, is provided. The proposed scheme guarantees asymptotic convergence to zero of the output regulation error coping with the system constraints and disturbances. A constructive and simple method, based on linear matrix inequalities, is proposed to compute the controller gains. Some simulation results illustrate the feasibility of the proposed scheme.