Mixed H2/H∞ Output Trace Control for Complex Water Network

ABSTRACT This paper addresses output‐tracking control for complex urban water distribution networks with multiple time‐varying delays and develops a feedback synthesis framework based on linear matrix inequalities (LMI). Guided by the network's interconnection structure, the physical system is abstracted as a discrete‐time multi‐delay model. An augmented Lyapunov–Krasovskii functional with free‐weighting matrices is constructed to derive LMI sufficient conditions that guarantee asymptotic stability and provide upper bounds on the mixed tracking performance. These conditions in turn enable a convex controller‐synthesis procedure. Numerical simulations demonstrate fast, robust, and energy‐efficient reference tracking in the presence of multiple delays and exogenous disturbances. The results furnish a computable, implementation‐ready design tool for pressure regulation and operational scheduling in urban water‐supply systems, with strong prospects for engineering deployment.