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—In this paper, a fuzzy impulsive control strategy is proposed. The state vectors that the impulsive controller resets to are determined so that the state vectors of interpolative low-pass sigma–delta modulators (SDMs) are bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are,… (More)

It has been established that a class of bandpass sigma delta modulators (SDMs) may exhibit state space dynamics which are represented by elliptical or fractal patterns confined within trapezoidal regions when the system matrices are marginally stable. In this paper, it is found that fractal patterns may also be exhibited in the phase plane when the system… (More)

In this paper, it is found that the weights of a perceptron are bounded for all initial weights if there exists a nonempty set of initial weights that the weights of the perceptron are bounded. Hence, the boundedness condition of the weights of the perceptron is independent of the initial weights. Also, a necessary and sufficient condition for the weights… (More)

In this letter, the normalized histogram of the state variable of first-order digital filters with two's complement arithmetic is investigated. When the pole of the digital filter is between 1 and 2, it is found that the possibility of occurrence of the state variable in certain region is close to zero no matter what the initial condition is. Some analytic… (More)

⎯It has been established that the class of bandpass sigma delta modulators (SDMs) with single bit quantizers could exhibit state space dynamics represented by elliptic or fractal patterns confined within trapezoidal regions. In this letter, we find that elliptical fractal patterns may also occur in bandpass SDMs with multi-bit quantizers, even for the case… (More)

—In this brief, a near allpass strictly stable minimal phase real valued rational IIR filter is designed so that the maximum absolute phase error is minimized subject to a specification on the maximum absolute allpass error. This problem is actually a minimax nonsmooth optimization problem subject to both linear and quadratic functional inequality… (More)