L2-L∞ Filter Design With Adjustable Convergence Rate for Linear Stochastic Systems
针对线性随机时变时滞系统，提出一种基于滤波器速度约束的L2-L∞滤波器设计新准则，可同时保证滤波误差系统稳定性和估计收敛速度，并通过仿真验证有效性。
The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}-\mathcal {L}_{\infty }$ </tex-math></inline-formula> filter design for linear stochastic time-varying delay systems based on the filter velocity constraint is considered in this dissertation. Different from existing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}\,-\,\mathcal {L}_{\infty }$ </tex-math></inline-formula> performance analysis and filter design, a new criterion is proposed to make a more accurate judgment, which can not only guarantee the stability of the filtering error system with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}-\mathcal {L}_{\infty }$ </tex-math></inline-formula> performance level but also can estimate the convergence speed of the filter. The ideal filter should has the same convergence speed as the original system, so as to ensure the rapid convergence of the error system, but also not to reduce the anti-interference ability and increase the bandwidth of the filter system. By the new filter design method, an ideal filter can be designed, which can regulate the convergence speed of the filter system to the desired effect. A simulation instance is provided to exhibit the validity of the new approach.