Robust control of systems with input and state constraints via LQG-balancing

A novel approach to robust control of systems with input and state constraints is suggested. First, a robustification is obtained by embedding the nominal model in a whole class of extended systems. This embedding is suggested as an `inverse´ to the model reduction technique based on balanced truncation. LQG (linear quadratic Gaussian) balancing is favored because of its `naturalness´ with respect to the given constraints. Open-loop balancing is not appropriate because of its restriction to stable systems. In the final step, a saturating controller is designed for the class of nonnominal systems based on positive invariance