基于LMI方法的线性不确定时滞系统鲁棒镇定

LMI-Based Robust Stabilization of Linear Uncertain Systems with Input Time-Delay

考虑同时具有状态时滞和输入时滞的参数不确定线性时滞系统的鲁棒镇定问题,其参数不确定性满足范数有界条件,而状态时滞和输入时滞均为时变有界形式.鲁棒镇定控制器采用无记忆状态反馈形式,用线性矩阵不等式(LMI)方法,给出了在该控制器作用下闭环系统鲁棒指数稳定的LMI形式的充分条件.所给出的判据不要求时滞导数小于1,降低了以往文献中稳定性条件的保守性,既适合于快时变时滞系统,也适合于慢时变时滞系统.最后,通过数值算例验证了所给鲁棒稳定性条件的有效性.

To robust stabilization problems for a linear uncertain system with parametric uncertainties, state delay and input delay were considered, where the parametric uncertainties are norm-bounded, and the state and input delays are time-varying and bounded. For robust stabilization of this system, a memoryless state-feedback robust stabilization controller was designed, and LMI-formed （linear matrix inequalities） sufficient conditions for robust exponential stability of the closed-loop system under the controller were given. These sufficient conditions don not require that the derivative of delays be less than 1, so they are less conservative than those in the current researches. Furthermore, they can be applied in both fast- and slow-varying time delay systems. Finally, a numerical example was given to demonstrate the validity of the proposed robust stability conditions.