An asymmetric Lyapunov function for linear systems with asymmetric actuator saturation
An asymmetric Lyapunov function for linear systems with asymmetric actuator saturation
复制标题
具有不对称执行器饱和的线性系统的不对称李亚普诺夫函数
DOI：
10.1002/rnc.3976
复制
发表时间：
2018
影响因子：
3.9
通讯作者：
Lin Zongli
中科院分区：
文献类型：
--
作者：
Li Yuanlong;Lin Zongli
针对非对称致动器饱和的线性系统，提出了一种非对称Lyapunov函数估计吸引域和保证区域L2增益域的方法。根据m个输入的符号，将输入空间划分为2m个区域。在每个区域内，具有不对称饱和输入的线性系统可以表示为具有对称死区的线性系统。对每个区域构造了包含系统状态和对称死区函数的增广状态向量的二次函数。由这些二次函数组成一个非对称Lyapunov函数。在此基础上，基于区域间交点的特殊性质，提出了2种广义非对称Lyapunov函数，降低了保守性。建立了一组条件，在这些条件下，这些非对称Lyapunov函数的水平集是收缩不变的，因此是吸引域的估计。导出了另一组条件，在这些条件下，水平集是具有保证区域L2增益的域的子集。基于这些条件，提出并求解了基于LMI的优化问题，以获得最大的水平集作为吸引域和具有保证区域L2增益的域的估计。仿真结果验证了该方法的有效性。
This paper proposes an asymmetric Lyapunov function approach to the estimation of the domain of attraction and the domain with a guaranteed regional L2 gain for a linear system subject to asymmetric actuator saturation. Depending on the sign of each of the m inputs, the input space is divided into 2m regions. In each region, the linear system with asymmetrically saturated inputs can be expressed as a linear system with symmetric dead zone. A quadratic function of the augmented state vector containing the system state and the symmetric dead‐zone function is constructed for each region. From these quadratic functions, an asymmetric Lyapunov function is composed. Furthermore, based on the special properties of the intersections between regions, 2 generalized asymmetric Lyapunov functions are proposed that lead to reduced conservativeness. A set of conditions are established under which the level sets of these asymmetric Lyapunov functions are contractively invariant and are thus estimates of the domain of attraction. Another set of conditions are derived under which the level sets are subsets of the domain with a guaranteed regional L2 gain. Based on these conditions, LMI‐based optimization problems are formulated and solved to obtain the largest level sets as the estimates of the domain of attraction and of the domain with a guaranteed regional L2 gain. Simulation results demonstrate the effectiveness of the proposed approach.