A mixed H2/H∞ control problem for sampled-data systems

A worst-case mixed H-2/H-infinity-optimal control problem is formulated and solved for sampled-data systems. By analogy with continuous and discrete mixed H-2/H-infinity problems, the solution can be formulated in terms of a parametrization of the optimal controller, and an associated parametric optimization problem. Characterizations of the optimal controller are derived both in terms of a set of synthesis equations and in the form of a convex optimization problem. An important property of the mixed H-2/H-infinity cost is its relation to a robust H-2 performance measure. The controller synthesis method can therefore be applied to the design of sampled-data controllers which achieve robust H(2 )performance for uncertain systems.