Design of LMI‐based sliding mode controller with an exponential policy for a class of underactuated systems

In this article, a novel sliding mode control (SMC) approach is proposed for the control of a class of underactuated systems which are featured as in cascaded form with external disturbances. The asymptotic stability conditions on the error dynamical system are expressed in the form of linear matrix inequalities. The control objective is to construct a controller such that would force the state trajectories to approach the sliding surface with an exponential policy. The proposed SMC has a simple structure because it is derived from the associated first‐order differential equation and is capable of handling system disturbances and nonlinearities. The effectiveness of the proposed control method is validated using intensive simulations. © 2014 Wiley Periodicals, Inc. Complexity 21: 117–124, 2016