Lyapunov‐based robust control design for a class of switching non‐linear systems subject to input saturation: application to engine control

Abstract

Control technique based on the well-known Takagi–Sugeno (T–S) models offers a powerful and systematic tool to cope with complex non-linear systems. This study presents a new method to design robust H ∞ controllers stabilising the switching uncertain and disturbed T–S systems subject to control input saturation. To this end, the input saturation is taken into account in the control design under its polytopic form. The Lyapunov stability theory is used to derive the design conditions, which are formulated as a linear matrix inequality (LMI) optimisation problem. The controller design amounts to solving a set of LMI conditions with some numerical tools. In comparison with previous results, the proposed method not only provides a simple and efficient design procedure to deal with a large class of input saturated non-linear systems but also leads to less conservative design conditions. Moreover, with a simple shape criterion, the proposed approach maximises also the estimated domain of attraction included inside the validity domain of the system. The validity of the proposed method is illustrated through academic as well as real industrial examples.