  The present work addresses a finite-horizon linear-quadratic optimal control
problem for uncertain systems driven by piecewise constant controls. The
precise values of the system parameters are unknown, but assumed to belong to a
finite set (i.e., there exist only finitely many possible models for the
plant). Uncertainty is dealt with using a min-max approach (i.e., we seek the
best control for the worst possible plant). The optimal control is derived
using a multi-model version of Lagrange's multipliers method, which specifies
the control in terms of a discrete-time Riccati equation and an optimization
problem over a simplex. A numerical algorithm for computing the optimal control
is proposed and tested by simulation.
