This study aims to design a robust state feedback controller for uncertain and perturbed linear systems with state constraints described by a polytope. This novel design incorporates the use of a composite barrier Lyapunov function (CBLF) and the convex hull of a set of ellipsoids inscribed in the given polytopic constraint set. The CBLF is used to ensure that this convex hull is an invariant set for the perturbed system states. Then, an optimization scheme is implemented to maximize the size of this invariant set to use it as a safe set. This is a set of initial conditions ensuring that the system solutions conform to the constraints for any subsequent time instant. Additionally, a minimal ultimate bound for the states is calculated to ensure asymptotic convergence to a region as close to the origin as possible. This region is characterized by a second convex hull of ellipsoids using the well‐known attractive ellipsoid method and the CBLF. Numerical simulations illustrate and compare the obtained results against a similar approach, considering the classical quadratic Lyapunov function, instead of the CBLF.

中文翻译：

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基于复合势垒Lyapunov函数的状态约束系统的鲁棒控制

这项研究的目的是为具有多态性描述的状态约束的不确定和扰动线性系统设计一个鲁棒的状态反馈控制器。这种新颖的设计结合了复合障碍Lyapunov函数（CBLF）的使用和给定的多面约束集内刻的一组椭球体的凸包。CBLF用于确保此凸包是受扰动系统状态的不变集。然后，实施优化方案以最大化此不变集的大小，以将其用作安全集。这是一组初始条件，可确保系统解决方案在任何后续时刻都符合约束条件。另外，计算状态的最小极限范围，以确保渐近收敛到尽可能靠近原点的区域。该区域的特征是使用众所周知的有吸引力的椭球方法和CBLF的椭球的第二个凸包。数值模拟说明并比较了采用类似二次方Lyapunov函数而不是CBLF的类似方法所获得的结果。