Fractional‐order filters have received extensive attention from international scholars because of their greater design freedom and continuously stepped stopband attenuation rate. Based on genetic algorithm (GA), this paper proposes an optimum design approach for fractional‐order Chebyshev lowpass filters that meet design specifications. The fractional order and ripples attenuation of the normalized Chebyshev lowpass filter are calculated according to specifications, the integer order in the Chebyshev polynomial is replaced with the calculated fractional order, and then the fractional‐order Chebyshev polynomial is substituted into the magnitude response of the normalized Chebyshev lowpass filter along with the ripples attenuation to achieve the ideal response. The transfer function parameters of a fractional‐order filter are optimized using GA to make the magnitude response approximate the ideal response described above. This completes the optimized design of a fractional‐order Chebyshev filter that meets specifications. Given three different sets of design specifications, the fractional‐order Chebyshev filter designed using the proposed method is compared with one designed by another method in the literature. Finally, design examples are presented, stability analysis and Pspice simulations are performed, and an actual circuit is constructed to illustrate the effectiveness of the proposed method.

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This work presents a new method to design the fractional-order linear phase filter based on the interior point algorithm. The transfer function of the fractional-order linear phase low-pass filter is derived from the general form of the fractional-order all-pole low-pass filter transfer function. The optimization problem of the phase-frequency characteristics of the fractional-order filter is modeled and solved. A detailed analysis of the stability and frequency domain of the optimized fractional-order linear-phase filters is presented. The active circuits for (1+α)-order filters are designed and simulated.

This note aims to establish the fast switching condition with average dwell time satisfying an upper bound. Important results are obtained on the behaviour of switched nonlinear dynamical systems. In specific, this note contributes in the following three aspects:(1) establish the condition of fast switching of switched nonlinear systems; (2) obtain the condition of arbitrary switching stability of switched nonlinear dynamical systems using a weak Lyapunov functions approach; and (3) prove the necessity of the average dwell time condition associated with the conventional multiple Lyapunov functions' framework.Jiqiang Wang et al. / IJAMML 4:2 (2016) [81][82][83][84][85][86][87][88][89][90][91] 82