Finite-time L 2-L∞ filtering for nonlinear stochastic systems based on a novel stochastic finite-time stability theorem

This paper presents a novel stochastic finite-time stability theorem and gives its application in the finite-time L-2-L-infinity filter design for nonlinear stochastic systems. Different form the frequently-used stochastic finite-time stability result, the proposed one does not require that all the states have the same fractional order exponent. Based on this result, a sufficient condition is given for nonlinear stochastic systems to possess the finite-time L-2-L-infinity performance with a prescribed gain. Further, an existence condition of the finite-time L-2-L-infinity filter with a prescribed disturbance attenuation level is given for nonlinear stochastic systems with external disturbance inputs. The effectiveness of the obtained results is illustrated by an example.