Optimal Feedback Stabilizing Control of Bounded Jacobian Discrete-Time Systems via Interval Observers

This paper addresses optimal feedback stabilizing control for bounded Jacobian nonlinear discrete-time (DT) systems with nonlinear observations, affected by state and process noise. Instead of directly stabilizing the uncertain system, we propose stabilizing a higher-dimensional interval observer whose states enclose the true system states. Our nonlinear control approach introduces additional flexibility compared to linear methods, compensating for system nonlinearities and allowing potentially tighter closed-loop intervals. We also establish a separation principle, enabling independent design of observer and control gains, and derive tractable linear matrix inequalities, resulting in a stable closed-loop system.