Robust $H_{\infty }$ Control of Discrete-Time Nonhomogenous Markovian Jump Systems via Multistep Lyapunov Function Approach
针对离散时间非齐次马尔可夫跳变线性系统，提出一种多步Lyapunov函数方法，推导出更宽松的稳定性判据和H∞性能分析，并设计鲁棒控制器，数值算例验证了该方法能有效提升干扰抑制性能。
This paper investigates the problems of robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for a class of discrete-time nonhomogenous Markovian jump linear systems (NMJLSs) by a multistep Lyapunov function (LF) approach. The proposed multistep LF is allowed to increase during the period of several sampling time step ahead of the current time within the Jump mode. First, a less conservative stability criterion is derived based on this multistep LF approach. Second, an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is analyzed under the multistep case by properly dealing with the knowledge of future states and exogenous noises. These two results are then employed to facilitate a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control design for NMJLSs, which yields a better disturbance attenuation performance as compared with the existing results. Numerical examples are included to elucidate the effectiveness of the developed results.