Robust Zonotopic Control

摘要

We propose a zonotopic framework for synthesizing a single robust state feedback controller that is certified to stabilize every plant inside a matrix zonotope, describing linearly varying parameters or parametric uncertainty. Common robust design strategies rely on checking many vertex models or on complex gain-scheduling, leading to high offline computation and implementation complexity. Our approach finds a single gain that is provably valid across the entire parameter domain, which is simpler to implement and can reduce conservatism by exploiting the structure of the zonotope. We formulate the robust synthesis as a single convex program tailored to the zonotope representation and incorporate practical performance requirements (actuator constraints, decay rate, disturbance attenuation) into the same synthesis stage. In numerical experiments on a representative 4-state example, our controller provides larger stability coverage across the parameter domain, attains comparable transient performance and control effort to more complex designs, and significantly reduces the number and scale of offline synthesis problems required by other robust approaches, compared to common-vertex gain, $H_{\infty}$, and $μ$-synthesis baselines.