Saturating control of unstable open loop systems

The problem of stabilization and null-controllability of open-loop unstable discrete-time multi-input systems with constraints on the states and the inputs is addressed. An analytic sufficient condition is derived. If it is satisfied by the linear controller for a given system and domain of initial conditions, then the constraints are not violated. The domain of feasible initial conditions is enlarged by allowing a saturating control. The saturation is with respect to the given quadratic constraints, and hence is not componentwise. The feasibility of using such a quadratic saturating control for problems with linear constraints is also examined by using suitable embeddings of the linear constraints in quadratic constraints. These ideas are illustrated by means of simulations