External stability of fractional-order control systems

The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. In terms of Lyapunov’s stability theory and the stability analysis of the integer-order linear control systems, the definitions of external stability for fractional-order control systems are presented. By using the theorems of the Mittag-Leffler function in two parameters, the necessary and sufficient conditions of external stability are directly derived. The illustrative examples and simulation results are also given.

Comprehensive assessment of real-time precise products from IGS analysis centers

Real-Time Precise Point Positioning(RT-PPP)has been one of the research hotspots in GNSS(Global Navigation Satellite System)community for decades.Real-time precise products of satellite orbits and clocks are the prerequisite for RT-PPP.Thus,it is of great importance to investigate the current multi-GNSS real-time precise products in State Space Representation(SSR)from diferent analysis centers.In this article,SSR products from 10 analysis centers are comprehensively evaluated by comparing them with the fnal products and performing the kinematic PPP.The results show that analysis centers CNES(Centre National D’Etudes Spatiales)and WHU(GNSS Research Center of Wuhan University)provide the most complete products with the best quality.Concerning the accuracy of real-time products for the GNSSs,the accuracies of orbit and clock products are better than 5 cm and 0.15 ns,respectively,for Global Positioning System(GPS),followed by Galileo navigation satellite system(Galileo),BeiDou-3 Navigation Satellite System(BDS-3),GLObal NAvigation Satellite System(GLONASS),and BeiDou-2 Navigation Satellite System(BDS-2).Meanwhile,the results of the RT-PPP with quad-system show that the positioning accuracies are 1.76,1.12 and 2.68 cm in east,north,and up directions,respectively,and the convergence time to 0.1,0.1,0.2 m for corresponding directions is 15.35 min.

Synchronization of switched Boolean networks with impulsive effects

This paper studies the state/output synchronization of switched Boolean networks （SBNs） with impulsive effects via the algebraic state space representation （ASSR） approach. First, an algebraic form is established for SBNs with impulsive effects via ASSR. Second, based on the algebraic form, some necessary and sufficient conditions are presented for the state/output synchronization of SBNs with impulsive effects under arbitrary switching signals. Third, two special kinds of switching signals, that is, free switching signal and feedback switching signal, are considered for the state synchroniza-tion of SBNs with impulsive effects. Finally, two illustrative examples are worked out to show the effectiveness of the obtained results.

Models and performance of SBAS and PPP of BDS

Satellite Based Augmentation System(SBAS)is one of the services provided by the BeiDou Navigation Satellite System(BDS).It broadcasts four types of diferential corrections to improve user application performance.These corrections include the State Space Representation(SSR)based satellite orbit/clock corrections and ionospheric grid corrections,and the Observation Space Representation(OSR)based partition comprehensive corrections.The algorithms generating these SBAS corrections are not introduced in previous researches,and the user SBAS positioning performance with the contribution of BDS-3 has not been evaluated.In this paper,we present the BDS SBAS algorithms for these diferential corrections in detail.Four types of Precise Point Positioning(PPP)function models for BDS Dual-Frequency(DF)and Single-Frequency(SF)users using the OSR and SSR parameters are also proposed.One week of data in 2020 is collected at 20 reference stations including the observations of both BeiDou-2 Navigation Satellite System(BDS-2)and BeiDou-3 Navigation Satellite System(BDS-3)satellites,and the PPP under various scenarios are performed using all the datasets and the BDS SBAS broadcast corrections.The results show that the performance of BDS-2/BDS-3 combination is superior to that of BDS-2 only constellation.The positioning errors in Root Mean Square(RMS)for the static DF PPP are better than 8 cm/15 cm in horizontal/vertical directions,while for the static SF PPP are 11 cm/24 cm.In the scenarios of simulated kinematic PPP,three Dimension(3D)positioning errors can reach 0.5 m in less than 10 min for the DF PPP and 30 min for the SF PPP,and the RMSs of the DF and SF PPP are better than 17 cm/21 cm and 20 cm/32 cm in horizontal/vertical directions.In a real-time single-and dual-frequency kinematic positioning test,the positioning errors of all three components can reach 0.5 m within 30 min,and the positioning accuracy after solution convergence in the N,E and U directions is better than 0.3 m.