Control of Cutting Systems with Markovian Jump Parameters
具有马氏跳跃参数的切削加工系统控制问题研究

This paper is concerned with exponential stability of a single-tool orthogonal cutting system, which is modelled as a Markovian jump system with time-varying delay. A new method using varying feed rate control is presented. Sufficient conditions for exponential stability in the mean square sense are obtained using the Lyapunov-Krasovskii functional (LKF) method. Furthermore, a robust stochastic stability criterion is established for the discussed system, in which the system matrices and the mode transition rate are partially known. The effects of delay parameters on the exponential convergence rate of the system states are also discussed. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.