带有扰动的变时滞离散系统可达集估计

研究了在有界峰值扰动下变时滞离散系统的可达集估计和状态反馈控制器设计问题。首先，选取适当的Lyapunov-Krasovkii泛函，利用线性矩阵不等式，得到界定系统可达集的充分条件，即一个包含非凸标量的时滞相关结果。在系统初始值不为零的情况下，这些条件保证了包含系统状态的椭球体的存在性。其次，在可达集估计过程中，通过设计状态反馈控制器使所确定的椭球包含闭环系统的可达集。随后，为使所估计的椭球体尽可能小，将求解最小椭球问题转化为一个具有矩阵不等式约束的优化问题。最后，通过数值算例验证所得结果的有效性。

Reachable set estimation for discrete-time systems with time-varying delay and disturbances

The problem of reachable set estimation and state-feedback controller design for discrete-time systems with time-varying delay under bounded peak disturbances was concerned. Firstly, by choosing appropriate Lyapunov-Krasovkii functional and based on the linear matrix inequality, a sufficient condition was obtained to bound the reachable set of closed-loop systems, that was, a delay-dependent result containing one nonconvex scalar. When the initial value of the system was not zero, these conditions guaranteed the existence of the ellipsoid containing the system state. Secondly, in the process of reachable set estimation, a state-feedback controller was designed to determine ellipsoid which contained the reachable set of the closed-loop system. Thirdly, in order to make the estimated ellipsoid as small as possible, the minimum ellipsoid problem was transformed into an optimization problem with matrix inequality constraints. Finally, numerical examples were given to verify the effectiveness of the obtained results.