This paper considers the problem of designing a shifting state-feedback controller via quadratic parameter-dependent Lyapunov functions (QPDLFs) for systems subject to symmetric time-varying saturations. By means of the linear parameter varying (LPV) framework and the use of the shifting paradigm and the ellipsoidal invariant theory, it is shown that the solution to this problem can be expressed with linear matrix inequalities (LMIs) which can efficiently be solved via available solvers. Specifically, three hyper-ellipsoidal regions are defined in the state-space domain for ensuring that the control action remains in the linearity region of the actuators where saturation does not occur. Furthermore, the closed-loop convergence speed is regulated online according to the instantaneous saturation limit values through the shifting paradigm concept. The main characteristics of the proposed approach are validated by means of two illustrative examples.

本文考虑了通过二次参数相关的 Lyapunov 函数 (QPDLF) 为受对称时变饱和度影响的系统设计移动状态反馈控制器的问题。通过线性参数变化 (LPV) 框架和移位范式和椭球不变理论的使用，表明该问题的解决方案可以用线性矩阵不等式 (LMI) 表示，可以通过可用的方法有效地解决求解器。具体而言，在状态空间域中定义了三个超椭圆区域，以确保控制动作保持在不发生饱和的执行器的线性区域中。此外，通过转移范式概念，根据瞬时饱和极限值在线调节闭环收敛速度。