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In this article, a solution to the output tracking problem is proposed for linear systems affected by external disturbances. The proposed robust control approach has a discontinuous integral term that provides exact and finite‐time convergence to zero of the output tracking error in the presence of external disturbances. The proposed nonlinear controller is non‐homogeneous. A constructive method to compute the controller gains is provided in order to ensure the convergence to zero of the output tracking error. Some simulation results are presented in order to illustrate the feasibility of the proposed robust control approach.

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.