LMI & BMI technics for the design of a PI control for irrigation channels

This paper considers the problem of control design for a nonlinear distributed parameter system in infinite dimension which is described by hyperbolic Partial Differential Equations (PDEs) of de Saint-Venant. For describing the dynamic of this nonlinear system over a wide operating range, the Multi-Models approach, which takes into account Linear Time Invariant (LTI) models defined around a set of operating points, has been used. By means of an Internal Model Boundary Control (IMBC), a new design of Proportional Integral (PI) feedback is performed through Bilinear Matrix Inequality (BMI) and Linear Matrix Inequality (LMI) technique. The new results have been simulated and also compared to the previous results, illustrating the new theoretical contribution.