不确定线性奇异时滞系统的时滞相关型h_2c∞_变结构控制

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1、山东大学硕士学位论文thehelpofLMI，wegiveadelay·dependentsufficientconditionwhichensurethattheslidingmodedynamicsrestrictedtotheswitchingsurfaceisnotonlyregular，impulsefreebutinternallystablewithdisturbanceattenuation．Astatefeedbackvariablestructurecontrollerisgivenaswell．Wealso舀veanexplicitformulaof

2、suchlinearswitchingsurface，togetherwithadesignexample．Inthesecondsection，wediscussauncertainsingulartime—delaysystem：lE±(t)=(A+△Aj互0)+【Aa+△Ad)]z0一下)+[B+△曰】u0)+【F+AFlw(t){。(t)=Cx(t)l。(￡)=妒0)，t∈【一r，0]wherex(t)∈R“isthestate，u(t)∈R”isthecontrolinput，z(t)∈RPistheoutput．W∈R‘isthesquare-integrab

3、leexternaldisturbancewhosenormisboundedbytheknownscalar￡，i．e．，

4、Jw(t)I

5、≤￡．Delay7_isaknownpositivescalar．庐(t)∈e(【一7_，o]，R“)isacompatiblevectorvaluedcontinuousfunction．TheconstantmatricesE，A，Ad，B，CandFareofappropriatedimensions，rankB=m，rankE。P，0

6、e—invariantmatricesrepresentingnorm—boundeduncertaintiesandhavethefollowingforill△A

7、J≤P1，J

8、AAa

9、JS户2，liABIl≤P3，

10、

11、△Flf≤P4wherePi，i=1，．．．，4，areallknownpositiveconstants．ItgivesaslidingsurfaceQ={z：盯(。)=SEx=o)whereJ∈14⋯⋯‘IStobedesign-Regardingtheabovesystem，intheorem2wegiveadelay—dependentsuff

12、icientcon．dition，guaranteeingthattheequivalentsystemOiltheslidingsurfaceisregular，impulsefreeandinternallystablewithdisturbanceattenuation．㈠I小。，X0，TR-t-Y+YT>_o∽J]<0'⋯～山东大学硕士学位论文2222。。2222=≈==2======；：have80lutiOnSN，YandX>0，M>0，Q>0，R≥0，Z>0，dl>0，d2>0，A>0．WhereJ，Jand7raredescribed

13、attheback．A8umcientconditiongivenbytheorem2canbededucedtosolvabilityofLMIs．Wecan。出。mateLMIsbyMATLABsoftware．SwitchingparametermatrixScanbe0btainedbyS=LB2X～．Theorem3givesthevariablestructurecontroIIer．u(t)=一(SB)一一p(z(f))1SAx(t)一(sB)一1SAdx(t～T)黑SB川训，o)1

14、

15、(一alI’I⋯117=”Wherep(z(。))2≯+㈣㈨·㈣t)f』

16、+P2㈦t—r)¨+P3JJSoAx(t)+SoAdx(t一7．)扪【+zIISoFII+P49lISo吣Ip2^喇n(2，一(BrX“B)～～pi

17、

18、X一1

19、J，)JThiscontrollerensuresthattheninfinitetimeandstayOilit8yst8mstatetrajectorycanreachtheslidingsurfaceI“s。cti。n3，wegiveallexamplet。illustratethevalidity。f。uralgorithm删喊麓如吼甄Ⅶ一嘶耻m呱慨驴蛐妇=誊‰