模糊时滞系统的记忆状态反馈控制
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摘要
该文研究了Takagi-Sugeno (T-S)模糊时滞系统的稳定与镇定问题。首先,选择一个近期提出的基于辅助函数的积分不等式,以线性矩阵不等式(LMIs)形式给出了保守性较小的时滞依赖的稳定性准则。其次,结合Finsler引理,首次提出了基于前提不匹配技术的模糊记忆状态反馈控制器设计方法,该前提不匹配的记忆控制器不要求与模糊系统拥有相同的隶属函数和模糊规则数目。最后,给出两个仿真算例证明所提理论的先进性和有效性。
The problems of stability and stabilization of Takagi-Sugeno(T-S) fuzzy time-delay systems are investigated in this paper. Firstly, less conservative delay-dependent stability criterion in terms of linear matrix inequalities(LMIs) is obtained by choosing a recently developed auxiliary function-based integral inequality.Secondly, combining with Finsler lemma, a fuzzy memory state feedback control design method is first time presented under the imperfect premise matching technique, while the memory controller under the imperfect premise matching technique does not be required to employ the same premise membership functions and the number of fuzzy rules as the fuzzy model. Finally, two numerical examples are given to show the progressiveness and effectiveness of the presented theory.
The problems of stability and stabilization of Takagi-Sugeno(T-S) fuzzy time-delay systems are investigated in this paper. Firstly, less conservative delay-dependent stability criterion in terms of linear matrix inequalities(LMIs) is obtained by choosing a recently developed auxiliary function-based integral inequality.Secondly, combining with Finsler lemma, a fuzzy memory state feedback control design method is first time presented under the imperfect premise matching technique, while the memory controller under the imperfect premise matching technique does not be required to employ the same premise membership functions and the number of fuzzy rules as the fuzzy model. Finally, two numerical examples are given to show the progressiveness and effectiveness of the presented theory.
引文
[1]KWON O M,PARK M J,PARK J H,et al.Stability and stabilization of TS fuzzy systems with time-varying delays via augmented Lyapunov-Krasovskii functionals[J].Information Sciences,2016,372:1-15.
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[4]MAHMOUDABADI P,SHASADEGHI M,ZAREI J.New stability and stabilization conditions for nonlinear systems with time-varying delay based on delay-partitioning approach[J].ISA Transactions,2017,70:46-52.
[5]LAM H K,LEUNG F H F.Stability analysis of fuzzymodel-based control systems[M].Berlin,Germany:Springer,2011.
[6]LI Xiao-mao,LAM H K,LIU Fu-cai,et al.Stability and stabilization analysis of positive polynomial fuzzy systems with time delay considering piecewise membership functions[J].IEEE Transactions on Fuzzy Systems,2017,25(4):958-971.
[7]ZHAO Tao,DIAN Song-yi.State feedback control for interval type-2 fuzzy systems with time-varying delay and unreliable communication links[J].IEEE Transactions on Fuzzy Systems,2018,26(2):951-966.
[8]姜偕富,费树岷.时滞线性系统的H∞控制[J].控制与决策,1999,14(6):712-715.JIANG Xie-fu,FEI shu-min.The H∞control of linear timedelay systems[J].Control and Decision,1999,14(6):712-715.
[9]ZHANG Zi-ye,LIN Chong,CHEN Bing.New stability and stabilization conditions for T-S fuzzy systems with time delay[J].Fuzzy Sets and Systems,2015,263:82-91.
[10]WANG Li-kui,LAM H K.A new approach to stability and stabilization analysis for continuous-time TakagiSugeno fuzzy systems with time delay[J].IEEETransactions on Fuzzy Systems,2018,26(4):2460-2465.
[11]PARK P G,LEE W I,LEE S Y.Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems[J].Journal of the Franklin Institute,2015,352(4):1378-1396.
[12]CHEN Yun,ZHENG Wei-xing.Exponential H∞filtering for stochastic Markovian jump systems with time delays[J].International Journal of Robust and Nonlinear Control,2014,24(4):625-643.
[13]LIU Fang,WU Min,HE Yong,et al.New delay-dependent stability criteria for T-S fuzzy systems with time-varying delay[J].Fuzzy Sets and Systems,2010,161(15):2033-2042.
[14]ZHANG Ze-jian,WANG Da-wei,GAO Xiao-zhi,et al.Improved delay-dependent stability analysis for uncertain TS fuzzy systems with time-varying delay[C]//12th International Conference on Fuzzy Systems and Knowledge Discovery(FSKD).[S.l.]:IEEE,2015:73-77.
[15]ZENG Hong-bing,PARK J H,XIA Jianwei,et al.Improved delay-dependent stability criteria for T-S fuzzy systems with time-varying delay[J].Applied Mathematics and Computation,2014,235:492-501.
[16]AN Ji-yao,WEN Gui-lin.Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach[J].Fuzzy Sets and Systems,2011,185(1):83-94.
[17]LIAN Zhi,HE Yong,ZHANG Chuan-ke,et al.Further robust stability analysis for uncertain Takagi-Sugeno fuzzy systems with time-varying delay via relaxed integral inequality[J].Information Sciences,2017,409:139-150.
[18]CAO Yong-yan,FRANK P M.Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach[J].IEEE Transactions on Fuzzy Systems,2000,8(2):200-211.
[19]LIEN Chang-hua.Stabilization for uncertain TakagiSugeno fuzzy systems with time-varying delays and bounded uncertainties[J].Chaos,Solitons&Fractals,2007,32(2):645-652.
[20]TENG Long,WANG You-yi,CAI Wen-jian,et al.Fuzzy model predictive control of discrete systems with time-varying delay and disturbances[J].IEEETransactions on Fuzzy Systems,2018,26(3):1192-1206.
[2]GU K,NICULESCU S I.Survey on recent results in the stability and control of time-delay systems[J].Journal of Dynamic Systems,Measurement,and Control,2003,125(2):158-165.
[3]ZHANG Xian-ming,HAN Qing-long,SEURET A,et al.An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay[J].Automatica,2017,84:221-226.
[4]MAHMOUDABADI P,SHASADEGHI M,ZAREI J.New stability and stabilization conditions for nonlinear systems with time-varying delay based on delay-partitioning approach[J].ISA Transactions,2017,70:46-52.
[5]LAM H K,LEUNG F H F.Stability analysis of fuzzymodel-based control systems[M].Berlin,Germany:Springer,2011.
[6]LI Xiao-mao,LAM H K,LIU Fu-cai,et al.Stability and stabilization analysis of positive polynomial fuzzy systems with time delay considering piecewise membership functions[J].IEEE Transactions on Fuzzy Systems,2017,25(4):958-971.
[7]ZHAO Tao,DIAN Song-yi.State feedback control for interval type-2 fuzzy systems with time-varying delay and unreliable communication links[J].IEEE Transactions on Fuzzy Systems,2018,26(2):951-966.
[8]姜偕富,费树岷.时滞线性系统的H∞控制[J].控制与决策,1999,14(6):712-715.JIANG Xie-fu,FEI shu-min.The H∞control of linear timedelay systems[J].Control and Decision,1999,14(6):712-715.
[9]ZHANG Zi-ye,LIN Chong,CHEN Bing.New stability and stabilization conditions for T-S fuzzy systems with time delay[J].Fuzzy Sets and Systems,2015,263:82-91.
[10]WANG Li-kui,LAM H K.A new approach to stability and stabilization analysis for continuous-time TakagiSugeno fuzzy systems with time delay[J].IEEETransactions on Fuzzy Systems,2018,26(4):2460-2465.
[11]PARK P G,LEE W I,LEE S Y.Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems[J].Journal of the Franklin Institute,2015,352(4):1378-1396.
[12]CHEN Yun,ZHENG Wei-xing.Exponential H∞filtering for stochastic Markovian jump systems with time delays[J].International Journal of Robust and Nonlinear Control,2014,24(4):625-643.
[13]LIU Fang,WU Min,HE Yong,et al.New delay-dependent stability criteria for T-S fuzzy systems with time-varying delay[J].Fuzzy Sets and Systems,2010,161(15):2033-2042.
[14]ZHANG Ze-jian,WANG Da-wei,GAO Xiao-zhi,et al.Improved delay-dependent stability analysis for uncertain TS fuzzy systems with time-varying delay[C]//12th International Conference on Fuzzy Systems and Knowledge Discovery(FSKD).[S.l.]:IEEE,2015:73-77.
[15]ZENG Hong-bing,PARK J H,XIA Jianwei,et al.Improved delay-dependent stability criteria for T-S fuzzy systems with time-varying delay[J].Applied Mathematics and Computation,2014,235:492-501.
[16]AN Ji-yao,WEN Gui-lin.Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach[J].Fuzzy Sets and Systems,2011,185(1):83-94.
[17]LIAN Zhi,HE Yong,ZHANG Chuan-ke,et al.Further robust stability analysis for uncertain Takagi-Sugeno fuzzy systems with time-varying delay via relaxed integral inequality[J].Information Sciences,2017,409:139-150.
[18]CAO Yong-yan,FRANK P M.Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach[J].IEEE Transactions on Fuzzy Systems,2000,8(2):200-211.
[19]LIEN Chang-hua.Stabilization for uncertain TakagiSugeno fuzzy systems with time-varying delays and bounded uncertainties[J].Chaos,Solitons&Fractals,2007,32(2):645-652.
[20]TENG Long,WANG You-yi,CAI Wen-jian,et al.Fuzzy model predictive control of discrete systems with time-varying delay and disturbances[J].IEEETransactions on Fuzzy Systems,2018,26(3):1192-1206.