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Time Delay Systems Part 11

Tham khảo tài liệu 'time delay systems part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Recent Progress in Synchronization of Multiple Time Delay Systems 189 adopted so as the relation in Eq. 21 is fulfilled in pair. Note from Eqs. 19 and 21 that only some components in the master s and slave s equations are selected for such the relations. Therefore Eq. 20 reduces to dA P . d -aA y nif xTi Td At ATi 22 By applying the Krasovskii-Lyapunov theory Hale Lunel 1993 Krasovskii 1963 to the case of multiple time-delays the sufficient condition to achieve limt . A t 0 from Eq. 22 is expressed as P a y niI sup f xT Td 23 i 1 where sup If . I stands for the supreme limit of If . . It is easy to see that the sufficicent condition for synchronization is obtained under a series of assumptions. Noticably the linear delayed system of A given in Eq. 22 is with time-dependent coefficients. The specific example shown in Section 4 with coupled modified Mackey-Glass systems will demonstrate and verify for the case. Next combination synchronous scheme will be presented there the mentioned synchronous scheme of coupled MTDSs is associated with projective one. 3.1.2 Projective-lag synchronization In this section the lag synchronization of coupled MTDSs is investigated in a way that the master s and slave s state variables correlate each other upon a scale factor. The dynamical equations for synchronous system are defined in Eqs. 12 - 14 . The desired projective-lag manifold is described by ay t bx t - Td 24 where a and b are nonzero real numbers and Td is the time lag by which the state variable of the master is retarded in comparison with that of the slave. The synchronization error can be written as A t ay t - bx t - Td 25 And dynamics of synchronization error is dA to - bịx Tl. 26 dt dt dt By substituting appropriate components to Eq. 26 the dynamics of synchronization error can be rewritten as dA a dt P Q -ay y nif yr y kjf xTp j -b P -ax t - Td y mif T Td i 1 j 1 i 1 27 Moreover yTi can be deduced from Eq. 25 as . _ bxT T at Vt ----- ----- a 28 190 Time-Delay Systems .