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H2 deconvolution fixed-lag smoothing for linear systems with multiplicative noises

The paper is dealt with the H2 fixed-lag deconvolution smoothing problem for linear systems. The problem is different from the standard H2 deconvolution filter or smoother, since the system is disturbed with multiplicative noises. Furthermore, multiplicative noises both occur in the system state equation and the observation equations. The H2 fixed-lag deconvolution smoother is given by solving Riccati equations and Lyapunov equation based on the projection theorem and innovation analysis. An numerical example is give to show the efficiency of the proposed H2 fixed-lag deconvolution smoother.