H∞H∞ model predictive control for discrete-time switched linear systems with application to drinking water supply network

• We propose a MPC methodology for switched linear systems with disturbances under an arbitrary switching law.
• We introduce a mixed H2/H∞H2/H∞ controller to guarantee performance and robustness.
• We obtain less conservative LMIs stability conditions.
• The theoretical results are applied in a drinking water supply network system.

This paper investigates the problem of a mixed H2/H∞H2/H∞ model predictive control (MPC) for a class of discrete-time switched linear systems in the presence of constraints on the states and inputs and with norm bounded disturbances. The objective is to minimize the upper bound of an infinite horizon cost function subject to a terminal inequality by using induced L2L2-norm bound. This work is an extension of the MPC approach proposed in Kothare et al. (1996) to switched systems under arbitrary switching law and with additive disturbances. The switched structure of the system is taken into account and by using some mathematical tools, the predictive controller design problem is turned into a Linear Matrix Inequalities (LMIs) feasibility problem. Finally, the main results of this method are applied to a drinking water supply network (DWSN). More precisely, a MPC strategy to regulate the water storage in each tank, in the presence of physical structural modifications, is proposed. Simulation results are proposed to show the good convergence properties of the control.