正切换系统状态依赖切换信号的分析与设计

Switching signal design is one of basic problems in study of switched systems. The state-dependent switching is an important technique in switching signal design. For general switched systems, the state-dependent-based results are quite abundant. However, for positive switched systems, the research based on state-dependent signals is just at the very beginning. The main reason lies in that the state space of positive switched systems is restricted in the nonnegative orthant, which will drive a significant change in switching signal design and raise some new challenges for our studies. This proposal will address the following three aspects: First, discuss the stability of positive switched systems when the state-dependent switching signals are given. Second, design the state-dependent switching signals to stabilize positive switched systems if the switching signals are unknown. Third, explore the essential relationships between stabilization and system structure for positive switched systems, and establish the equivalent conditions for system stabilization. This project is based on the research frontiers. The achievement of this project will perfect the theory of positive switched systems and provide the theoretical guidance for future work and a lot of application problems.

切换信号设计是切换系统研究的基本问题之一。状态依赖切换是切换信号设计的重要技术手段之一。对于一般切换系统而言，基于状态依赖切换的研究成果已经较为丰富。然而，基于状态依赖切换下正切换系统的研究才处于起步阶段，其原因在于状态空间被限制在非负象限，将导致状态依赖切换信号的设计发生根本性的变化，同时也给研究工作提出了新的挑战。本项目重点研究三个方面的问题：一、给定状态依赖切换信号，探讨正切换系统的稳定性。二、在切换信号未知的情况下，设计状态依赖切换信号镇定正切换系统。三、揭示正切换系统镇定性与系统结构之间的本质关系，进而建立系统可镇定的等价条件。本项目立足于前沿课题，其完成将有助于完善正切换系统理论，为后继研究和大量应用问题提供理论指导。

切换信号设计是切换系统研究的基本问题之一。状态依赖切换是切换信号设计的重要技术手段。基于状态依赖切换下正切换系统的研究才处于起步阶段，其原因在于状态空间被限制在非负象限，将导致状态依赖切换信号的设计发生根本性的变化，同时也给研究工作提出了新的挑战。此外，随着数字化时代的快速发展，在控制领域中引入网络传输媒介势在必行，网络传输的介入也增加了切换系统理论分析的复杂度。网络传输中考虑到信号在传感器到控制器和控制器到执行器中的传输依赖于网络通讯，可能分别受到DoS攻击，这使得切换系统采样的状态和切换信号将因为受到黑客的攻击存在丢包的风险。对于切换系统所做工作如下：一、基于Drazin逆构造新的投影算子对给定切换信号和任意切换下切换退化系统的正性和稳定性研究。二、离散线性切换系统遭受双信道拒绝服务攻击下的事件触发控制和稳定性研究。三、在遭受拒绝服务攻击下，对连续网络切换系统的混杂触发安全控制和稳定性问题研究。四、分式布朗运动噪声驱动下具有脉冲时滞的随机微分方程的p阶矩指数稳定和均方有界问题研究。