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Tham khảo tài liệu 'time delay systems part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Decentralized Adaptive Stabilization for Large-Scale Systems with Unknown Time-Delay 129 the unknown scalar function Tj t denotes any nonnegative continuous and bounded time-varying delay satisfying T t Tj 1 4 where Tj are known constants. For each decoupled local system we make the following assumptions. Assumption 1 The triple Ai bi Ci are completely controllable and observable. Assumption 2 For every 1 i N the polynomial bi m.smi bi is bi 0 is Hurwitz. The sign of bim and the relative degree Pi n mi are known. Assumption 3 The nonlinear interaction terms satisfy fij t yj l Yijfj t yj yj 5 where Yij are constants denoting the strength of interactions and fj yj j 1 2 . N are known positive functions and differentiable at least Pi times. Assumption 4 The unknown functions hij yj t satisfy the following properties hij yj t jj yj t yj 6 where hj are known positive functions and differentiable at least Pi times and fjare positive constants. Remark 1. The effects of the nonlinear interactions fij and time-delay functions hij from other subsystems to a local subsystem are bounded by functions of the output of this subsystem. With these conditions it is possible for the designed local controller to stabilize the interconnected systems with arbitrary strong subsystem interactions and time-delays. The control objective is to design a decentralized adaptive stabilizer for a large scale system 1 with unknown time-varying delay satisfying Assumptions 1-4 such that the closed-loop system is stable. 3. Design of adaptive controllers 3.1 Local state estimation filters In this section decentralized filters using only local input and output will be designed to estimate the unmeasured states of each local system. For the ith subsystem we design the filters as v i i Ai 0vi i. eni ni i ui 1 0 . mi 7 0 Ai oCi o ky 8 S i A-ifiBi t y 9 where Vj 6 Tn i 0 Tn Si yn r the vector ki kj 1 . ki ni T b n is chosen such that the matrix Ai 0 Ai ki e . 1 T is Hurwitz and ei k denotes the kth .