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With saturating actuators Robust control of multi-delay systems

z (£) +2 Σz (£) PA (£) z (£ a di (£))+ 2x (t) P (B4-AB (t)) rl (t) of a Σ a '(£ a ( £)) R (£ a) 1N (z (£),£) ≤ XT (£) w1z (£) + Σz (£ a dl (£))( I + a7ETE ~ R) z (£ A d ( £)) + z (£) P (B + AB (£))( B + AB) Pz (£) (5) Wl-AP + P_A + ÷ (1 + a) KBP + Si. N Report (1 + a) PBK + ΣR + oral EE. + I a 1 ~ Pa. HHTP + PfΣHH +1 H + Die A) P + special (1 +) KE [EK4-1 (1mO-) KK. Suppose that there exists a scalar £> 0 and positive definite symmetric matrix Q> 0,ropa ed hardy, makes the following inequality to meet BB + BE [(el-E: 1) ~ E6B + eH6H ≤ Q (6) of which £ J-E6E> 0 (7) Application Lemma 2 can be (B + △ B (£))( B + AB (T)) ≤ Q. Order R-J + mouth EE, by (5) have: (z (£),£) ≤ z '(£) Ew + PQP] z (£) for a 37' (t) W2z (£),tory burch uk, W2 One AP + PA + jump (1 + a) KBP + b (11 boats K + + aE [E + P. HaH +1 (1 + HH + NA + Q) p + special (1 +) KE [EK4-1 (1 a) KK . If there are positive definite symmetric matrices P,ed hardy brasil, Q, and scalar matrix K> 0, fl,christian louboutin,> 0 (A 1,2, ... N),fred perry paris, and £> 0 satisfy the inequality (6), (7) and w < 0, then for all admissible uncertainties, (z (£),£) ≤ a llz (£) ll. closed-loop system (4) is the robust stabilization, that is, the original uncertain time-delay system (1) is robust stabilizable. introduce new variables X-P ~, and let W. a XwX, then w <0 is equivalent to w. <0. ORDER Y-KX, and apply the Schur lemma, we know that inequality ( 6), (7) and w. <0 is equivalent to linear matrix inequalities (2), (3) .3 numerical example consider the linear uncertain time-delay system (1), where the nonlinear actuator saturation Fan interval [1 / 3, 1], assuming the remaining parameters are A [;。]' At a [b: A] 'Az A [a. 0.] v. H [。。]' Et a [: ], (fn'l, 2,6) d1 (£) a 0.1e_., d2 (t) a 0.1sint, r = 1. Guang sin (£) 0] F (t) a lI, i = n, 1. 2, bl. cos (t)] by Theorem using MATLAB LMI toolbox in the available x one 『.0 · 040-0 · 002], L a 0.00520.0615. J.r 10 .0384-0.00973 V-lI1 one. l1 ● - 0.00970.0341 J. Kwong a 2.8933-0.40103K-YX a 1 '. I.L a 0.50 l40 · 5134J 【Reference】 CHOUJH. H () RNGIR, CHENBS.Dynamicfeedbackcompensatorforuncertaintime-delaysystemscontainingsaturatingactuator [J]. IntJControl, 1989,49 (3) :961-968. NICUIESCUSI, DIONjM, DUGARDL.Robuststabi-lizationforuncertaintime-delaysystemscontainingsatura-tingactuators [-J]. IEEETransonAutoControl, 1996,4 l (5) 742-747. Su Hongye, Pan Honghua, Jiang accompany Gang, and so on. a class of nonlinear saturating actuator Robust control of uncertain time-delay system IJ]. Control and Decision, 2000,15 (1): 23 - 26. Wangju Feng, Sun Jitao. Delay Systems with Saturating Control Stability of I-J1. Tongji University (Natural Science), 2003,3 l ( Cool

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