摘要：In this paper, we concern the approaching condition of sliding mode control （SMC） with a Lipschitz switching surface that may be nonsmooth. New criteria on the relation between phase trajectories and an arbitrary Lipschitz continuous surface are examined firstly. Filippov＇s differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system with SMC. Compared with Filippov＇s criteria for only smooth surface, new criteria are proposed by utilizing the cone conditions that allow the surface to be nonsmooth. This result also yields a new approaching condition of SMC design. Based on the new approaching condition, we develop the sliding mode controller for a class of nonlinear single-input single-output （SISO） systems, of which the switching surface is designed Lips- chitz continuous for the nonsmooth sliding motion. Finally, we provide a numerical example to verify the new design method.

摘要：Time-varying frequency selective attenuation and colored noises are unfavorable characteristics of power line communication(PLC) channels of the low voltage *** overcome these disadvantages,a novel real-time dynamic spectrum management(DSM) algorithm in orthogonal frequency division multiplexing(OFDM)-based high-speed narrow-band power line communication(HNPLC) systems is proposed,and the corresponding FPGA circuit is designed and *** of the proposed DSM is validated with a large amount of network experiments under practical PLC *** the noise in each narrow subcarrier is approximately Gaussian,the proposed DSM adopts the BER/SER expression formulized via the AWGN channel to provide a handy and universal strategy for power *** real-time requirement is guaranteed by choosing subcarriers in group and employing the same modulation scheme within each *** measures are suitable for any modulation scheme no matter the system criterion is to maximize data rate or minimize power/*** design and hardware implementation of the proposed DSM are given with some flexible and efficient *** DSM circuit is carried out with Xilinx *** and practical experiments validate that the proposed real-time DSM significantly improves system performance.