Design of a Proportional Integral Control Using Operator Theory for Infinite Dimensional Hyperbolic Systems

This brief considers the control design of a nonlinear distributed parameter system in infinite dimension, described by the hyperbolic partial differential equations of de Saint-Venant. The nonlinear system dynamic is formulated by a multimodels approach over a wide operating range, where each local model is defined around a set of operating regimes. A new proportional integral feedback is designed and performed through bilinear operator inequality and linear operator inequality techniques for infinite dimensional systems. The new results have been simulated and also compared with previous results in finite and infinite dimension, to illustrate the new theoretical contribution.