Consider system (2.1), where h(t)= 1+sint,t∈?k∈N(2kπ,(2k+1)π),1,t∉?k∈N(2kπ,(2k+1)π),A=[10.50−1],A1=[0.50.10.10.5],B=[10].It is worth noting that ENMD-2076 the delay function h(t)h(t) is non-differentiable, AA is unstable, rank[B,AB]=1rank[B,AB]=1, i.e., [A,B][A,B] is uncontrollable. Given r=1,h1=1,h2=2, using LMI Toolbox in Matlab [15], the LMI (3.3) is feasible withP=[0.06060.01770.01770.0760],S1=[0.08590.07970.07970.1476],S2=[0.16900.07270.07270.2351],S3=[0.64060.02560.02560.6579],S4=[1.31800.64340.64341.5072],R1=[−0.3870−0.0967−0.0903−0.4152],R2=[−0.3831−0.0999−0.0927−0.4153]. The feedback control is then defined by u(t)=−11+‖[0.06060.0177]x(t)‖[0.06060.0177]x(t).Fig. 1 shows the simulation of the solutions x1(t)x1(t) and x2(t)x2(t) with the initial condition ?(t)=[1,2],t∈[−2,0].Fig. 1. The trajectories x1(t)x1(t), and x2(t)x2(t) of closed-loop system.Figure optionsDownload full-size imageDownload as PowerPoint slide4. ConclusionsIn arterioles paper, by using Lyapunov function method we have established new sufficient conditions for global stabilization of linear time-varying delay systems with bounded control. The sufficient conditions for designing feedback controllers are derived in terms of LMIs, which can be determined by utilizing MATLABs LMI Control Toolbox. A numerical example is given to show the validity of the proposed results.AcknowledgmentsThis work is supported by Chiang Mai University, Chiang Mai, Thailand and the National Foundation for Science and Technology Development, Viet Nam (No. 101.01.2014.35).
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