Output regulation for a cascaded network of 2 × 2 hyperbolic systems with PI controller

Abstract We are concerned with the PI control/regulation design for a cascaded network of multi systems governed by hyperbolic partial differential equations. The PI controllers have both control inputs and measured outputs situated on the junctions. The stability analysis of closed-loop network is carried out in the L 2 topology by using the Lyapunov direct method. Then the output regulation is proven based on the stability of closed-loop systems. We finally work out detailed PI controller design for a practical cascaded network of n hydraulic Saint-Venant models as well as numerical simulations to validate theoretical results.

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