L2-L∞ Filter Design With Adjustable Convergence Rate for Linear Stochastic Systems

Abstract

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.