In this letter, we propose a new H₂ smoother (H2S) with a finite impulse response (FIR) structure for discrete-time state-space signal models. This smoother is called an H₂ FIR smoother (H2FS). Constraints such as linearity, quasi-deadbeat property, FIR structure, and independence of the initial state information are required in advance to design H2FS that is optimal in the sense of H₂ performance criterion. It is shown that H2FS design problem can be converted into the convex programming problem written in terms of a linear matrix inequality (LMI) with a linear equality constraint. Simulation study illustrates that the proposed H2FS is more robust against uncertainties and faster in convergence than the conventional H2S.

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This letter presents a new mathematical expression for the excess mean-square error (EMSE) of the affine projection (AP) algorithm. The proposed expression explicitly shows the proportional relationship between the EMSE and the condition number of the input signals.

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We consider a problem of global asymptotic stabilization of a class of nonlinear systems that have the unknown linear growth rate. While the existing results only deal with one specified form of nonlinear systems, our proposed method includes both forms of triangular and feedforward nonlinear systems in a unified framework. The proposed controller has a dynamic gain mechanism which is selectively engaged based on the given nonlinear form. Then, the dynamic gain is adaptively tuned depending on the unknown linear growth rate.

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A two-quadrant CMOS current-mode plug-in divider using a compact 1/x device is presented. The mismatch errors of 1/x device cancel part of mismatch errors of the proposed divider. The simulation results indicate that the plug-in divider is feasible by the proposed approximation method. The adjustable 1/x device could be applied in difference ranges.

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We introduce (1-γ)-cyclic code and cyclic codes over the finite chain ring R. We prove that the Gray image of a linear (1-γ)-cyclic code over R of length n is a distance invariant quasi-cyclic code over F_p^k. We also prove that if (n, p)=1, then every code over F_p^k which is the Gray image of a cyclic code over R of length n is equivalent to a quasi-cyclic code.

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In this paper, a motion evaluation technique for rehabilitation training is introduced. Motion recognition technologies have been developed for determining matching motions in the training set. However, we need to measure how well and how much of the motion has been followed for training motion evaluation. We employed a Finite State Machine as a framework of motion evaluation. For similarity analysis, we used weighted angular value differences although any template matching algorithm may be used. For robustness under illumination changes, IR LED's and cameras with IR-pass filter were used. Developed technique was successfully used for rehabilitation training of the disabled. Therapists appraised the system as practically useful.

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