Definition and Utilization of the Null Controllable Region for Model Predictive Control of Multi-Input Linear Systems

The problem of guaranteeing stability from the entire null controllable region (NCR) for multi-input linear dynamical systems is addressed in the present manuscript. The proposed controller design is inspired by results for single input systems and generalized to multiple input systems. The approach relies on utilizing the level sets of the NCR as level sets of a Lyapunov function. A contractive constraint is incorporated into a model predictive control design, guaranteeing feasibility for any horizon length, and resulting in the NCR as the closed-loop stability region. The proposed method is illustrated using a simulation example.