Robust Finite-Time Guaranteed Cost Control for Positive Systems with Multiple Time Delays
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摘要
This paper deals with the finite-time guaranteed cost control problem for positive system with multiple time delays and bounded disturbance. By using Lyapunov-Krasovskii functional method,some new sufficient conditions for the design of a state feedback controller which makes the closedloop system finite-time stable and guarantees an adequate cost level of performance are derived. Two numerical examples are also given to show the effectiveness of the proposed method.
This paper deals with the finite-time guaranteed cost control problem for positive system with multiple time delays and bounded disturbance. By using Lyapunov-Krasovskii functional method,some new sufficient conditions for the design of a state feedback controller which makes the closedloop system finite-time stable and guarantees an adequate cost level of performance are derived. Two numerical examples are also given to show the effectiveness of the proposed method.
This paper deals with the finite-time guaranteed cost control problem for positive system with multiple time delays and bounded disturbance. By using Lyapunov-Krasovskii functional method,some new sufficient conditions for the design of a state feedback controller which makes the closedloop system finite-time stable and guarantees an adequate cost level of performance are derived. Two numerical examples are also given to show the effectiveness of the proposed method.
引文
[1]Farina E and Rinaldi S,Positive Linear Systems:Theory and Applications,New York,Wiley,2000.
[2]Kaczorek T,Positive 1D and 2D Systems,Springer-Verlag,London,2002.
[3]Zhang J S,Wang Y W,Xiao J W,et al.,Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure,International Journal of System Science,2016,47(4):946-955.
[4]Rami M A and Tadeo F,Controller synthesis for positive linear systems with bounded controls,IEEE Transactions on Circuits and Systems II:Express Briefs,2007,54(2):151-155.
[5]Shu Z,Lam J,and Gao H,Positive observers and dynamic output feedback controllers for interval positive linear systems,IEEE Transactions on Circuits and Systems I:Regular Papers,2008,55(10):3209-3222.
[6]Zhu S,Li Z,and Zhang C,Exponential stability analysis for positive systems with delays,IETControl Theory&Applications,2012,6(6):761-767.
[7]Zhu S,Meng M,and Zhang C,Exponential stability for positive systems with bounded timevarying delays and static output feedback stabilization,Journal of the Franklin Institute,2013,350(3):617-636.
[8]Phat V N and Sau N H,On exponential stability of linear singular positive delayed systems,Applied Mathematics Letters,2014,38:67-42.
[9]Zaidi I,Chaabane M,Tadeo F,et al.,Static state-feedback controller and observer design for interval positive systems with time delay,IEEE Transactions on Circuits and Systems II:Express Briefs,2015,62:506-510.
[10]Zhang J,Han Z,and Zhu F,L1-gain analysis and control synthesis of positive switched systems,International Journal of Systems Sciences,2015,46(12):2111-2121.
[11]Yang D,Liu Y,and Zhao J,Guaranteed cost control for switched LPV systems via parameter and state-dependent switching with dwell time and its application,Optimal Control Applications and Methods,2016,38(4):601-617.
[12]Du B,Lam J,Shu Z,et al.,On reachable sets for positive linear systems under constrained exogenous inputs,Automatica,2016,74:230-237.
[13]Dorato P,Short-Time Stability in Linear Time-Varying Systems,Tech.Rep.,Polytechnic Institute of Brooklyn,1961.
[14]Weiss L and Infante E F,Finite-time stability under perturbing forces and on product spaces,IEEE Transaction on Automatic Control,1967,12(1):54-59.
[15]Chen G and Yang Y,Finite-time stability of switched positive linear systems,International Journal of Robust and Nonlinear Control,2014,24:179-190.
[16]Zhang J,Han Z,and Wu H,Robust finite-time stability and stabilization of switched positive systems,IET Control Theory and Applications,2014,8(1):67-75.
[17]Zhang J,Han Z,and Wu H,Finite-time control and L1-gain analysis for positive switched systems,Optimal Control Applications and Methods,2015,36:550-565.
[18]Wen J,Nguang S K,Shi P,et al.,Finite-time stabilization of Markovian jump delay systems-a switching control approach,International Journal of Robust and Nonlinear Control,2017,27(2):298-318.
[19]Liu H and Lin X,Finite-time H∞control for a class of nonlinear system with time-varying delay,Neurocomputing,2015,149:1481-1489.
[20]Liu H,Shi P,Karimi H R,et al.,Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay,International Journal of Systems Sciences,2016,47(6):1433-1444.
[21]Rakkiyappan R,Velmurugan G,and Cao J,Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays,Nonlinear Dynamics,2014,78(4):2823-2836.
[22]Zhang J,Zhao X,and Chen Y,Finite-time stability and stabilization of fractional order positive switched systems,Circuits,Systems,and Signal Processing,2016,35(7):2450-2470.
[23]Hei X and Wu R,Finite-time stability of impulsive fractional-order systems with time-delay,Applied Mathematical Modelling,2016,40:4285-4290.
[24]Velmurugan G,Rakkiyappan R,and Cao J,Finite-time synchronization of fractional-order memristor-based neural networks with time delays,Neural Networks,2016,73:36-46.
[25]Ma Y,Wu B,and Wang Y E,Finite-time stability and finite-time boundedness of fractional order linear systems,Neurocomputing,2016,173:2076-2082.
[26]Wang F,Chen D,Zhang X,et al.,Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay,International Journal of Systems Science,2017,48(5):984-993.
[27]Li M and Wang J,Finite time stability of fractional delay differential equations,Applied Mathematics Letters,2017,64:170-176.
[28]Wu Y,Cao J,Alofi A,et al.,Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay,Neural Networks,2015,69:135-143.
[29]Wang S,Shi T,Zeng M,et al.,New results on robust finite-time boundedness of uncertain switched neural networks with time-varying delays,Neurocomputing,2015,151:522-530.
[30]Muthukumar P,Subramanian K,and Lakshmanan S,Robust finite time stabilization analysis for uncertain neural networks with leakage delay and probabilistic time-varying delays,Journal of the Franklin Institute,2016,353(16):4091-4113.
[31]Wang S,Shi T,Zhang L,et al.,Extended finite-time H∞control uncertain switched linear neural systems with time-varying delays,Neurocomputing,2015,152:377-387.
[32]Song J and He S,Finite-time H∞control for quasi-one-sided Lipschitz nonlinear systems,Neurocomputing,2015,149:1433-1439.
[33]Song J and He S,Robust finite-time H∞control for quasi-one-sided Lipschitz nonlinear systems via state feedback and output feedback,Journal of the Franklin Institute,2015,352:3250-3266.
[34]Lu R,Zhao S S,Wu Y,et al.,Finite-time bounded control for a class of stochastic nonlinear systems with randomly quantized measurements,Journal of the Franklin Institute,2016,353(17):4368-4383.
[35]Niamsup P and Phat V N,Robust finite-time control for linear time-varying delay systems with bounded control,Asian Journal of Control,2016,18(5):1-8.
[36]Niamsup P,Ratchgit K,and Phat V N,Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks,Neurocomputing,2015,160:281-286.
[37]Yan Z G,Zhang G,Wang J,et al.,State and output feedback finite-time guaranteed cost control of linear It o stochastic systems,Journal of Systems Science and Complexity,2015,28(4):813-829.
[38]Yan Z,Park J H,and Zhang W,Finite-time guaranteed cost control for It o stochastic Markovian jump systems with incomplete transition rates,International Journal of Robust and Nonlinear Control,2017,27:66-83.
[39]Cao X,Liu L,Fu Z,et al.,Guaranteed cost finite-time control for positive switched linear systems with time-varying delays,Journal of Control Science and Engineering,2017,Article ID 7051658,10 pages.
[40]Stojanovic S B,Further improvement in delay-dependent finite-time stability criteria for uncertain continuous-time systems with time-varying delays,IET Control Theory and Applications,2016,10(8):926-938.
[41]Kaczorek T,Stability of positive continuous-time linear systems with delays,Bulletin of the Polish Academy of Sciences:Technical Sciences,2009,57(4):395-398.
[42]Boyd S,Ghaoui L E,Feron E,et al.,Linear Matrix Inequalities in System and Control Theory,SIAM,Philadelphia,1994.
[43]Moon Y S,Park P G,and Kwon W H,Robust stabilization of uncertain input-delayed systems using reduction method,Automatica,2001,37:307-312.
[44]Yue D,Robust stabilization of uncertain systems with unknown input delay,Automatica,2004,40:331-336.
[45]De Oliveira M C,Geromel J C,and Bernusson J,Design of dynamic output feedback decentralized controllers via a separation procedure,International Journal of Control,2000,73(5):371-381.
[46]Thuan M V,Phat V N,and Trinh H,Dynamic output feedback guaranteed cost control for linear systems with interval time-varying delays in states and outputs,Applied Mathematics and Computation,2012,218:10697-10707.
[2]Kaczorek T,Positive 1D and 2D Systems,Springer-Verlag,London,2002.
[3]Zhang J S,Wang Y W,Xiao J W,et al.,Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure,International Journal of System Science,2016,47(4):946-955.
[4]Rami M A and Tadeo F,Controller synthesis for positive linear systems with bounded controls,IEEE Transactions on Circuits and Systems II:Express Briefs,2007,54(2):151-155.
[5]Shu Z,Lam J,and Gao H,Positive observers and dynamic output feedback controllers for interval positive linear systems,IEEE Transactions on Circuits and Systems I:Regular Papers,2008,55(10):3209-3222.
[6]Zhu S,Li Z,and Zhang C,Exponential stability analysis for positive systems with delays,IETControl Theory&Applications,2012,6(6):761-767.
[7]Zhu S,Meng M,and Zhang C,Exponential stability for positive systems with bounded timevarying delays and static output feedback stabilization,Journal of the Franklin Institute,2013,350(3):617-636.
[8]Phat V N and Sau N H,On exponential stability of linear singular positive delayed systems,Applied Mathematics Letters,2014,38:67-42.
[9]Zaidi I,Chaabane M,Tadeo F,et al.,Static state-feedback controller and observer design for interval positive systems with time delay,IEEE Transactions on Circuits and Systems II:Express Briefs,2015,62:506-510.
[10]Zhang J,Han Z,and Zhu F,L1-gain analysis and control synthesis of positive switched systems,International Journal of Systems Sciences,2015,46(12):2111-2121.
[11]Yang D,Liu Y,and Zhao J,Guaranteed cost control for switched LPV systems via parameter and state-dependent switching with dwell time and its application,Optimal Control Applications and Methods,2016,38(4):601-617.
[12]Du B,Lam J,Shu Z,et al.,On reachable sets for positive linear systems under constrained exogenous inputs,Automatica,2016,74:230-237.
[13]Dorato P,Short-Time Stability in Linear Time-Varying Systems,Tech.Rep.,Polytechnic Institute of Brooklyn,1961.
[14]Weiss L and Infante E F,Finite-time stability under perturbing forces and on product spaces,IEEE Transaction on Automatic Control,1967,12(1):54-59.
[15]Chen G and Yang Y,Finite-time stability of switched positive linear systems,International Journal of Robust and Nonlinear Control,2014,24:179-190.
[16]Zhang J,Han Z,and Wu H,Robust finite-time stability and stabilization of switched positive systems,IET Control Theory and Applications,2014,8(1):67-75.
[17]Zhang J,Han Z,and Wu H,Finite-time control and L1-gain analysis for positive switched systems,Optimal Control Applications and Methods,2015,36:550-565.
[18]Wen J,Nguang S K,Shi P,et al.,Finite-time stabilization of Markovian jump delay systems-a switching control approach,International Journal of Robust and Nonlinear Control,2017,27(2):298-318.
[19]Liu H and Lin X,Finite-time H∞control for a class of nonlinear system with time-varying delay,Neurocomputing,2015,149:1481-1489.
[20]Liu H,Shi P,Karimi H R,et al.,Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay,International Journal of Systems Sciences,2016,47(6):1433-1444.
[21]Rakkiyappan R,Velmurugan G,and Cao J,Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays,Nonlinear Dynamics,2014,78(4):2823-2836.
[22]Zhang J,Zhao X,and Chen Y,Finite-time stability and stabilization of fractional order positive switched systems,Circuits,Systems,and Signal Processing,2016,35(7):2450-2470.
[23]Hei X and Wu R,Finite-time stability of impulsive fractional-order systems with time-delay,Applied Mathematical Modelling,2016,40:4285-4290.
[24]Velmurugan G,Rakkiyappan R,and Cao J,Finite-time synchronization of fractional-order memristor-based neural networks with time delays,Neural Networks,2016,73:36-46.
[25]Ma Y,Wu B,and Wang Y E,Finite-time stability and finite-time boundedness of fractional order linear systems,Neurocomputing,2016,173:2076-2082.
[26]Wang F,Chen D,Zhang X,et al.,Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay,International Journal of Systems Science,2017,48(5):984-993.
[27]Li M and Wang J,Finite time stability of fractional delay differential equations,Applied Mathematics Letters,2017,64:170-176.
[28]Wu Y,Cao J,Alofi A,et al.,Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay,Neural Networks,2015,69:135-143.
[29]Wang S,Shi T,Zeng M,et al.,New results on robust finite-time boundedness of uncertain switched neural networks with time-varying delays,Neurocomputing,2015,151:522-530.
[30]Muthukumar P,Subramanian K,and Lakshmanan S,Robust finite time stabilization analysis for uncertain neural networks with leakage delay and probabilistic time-varying delays,Journal of the Franklin Institute,2016,353(16):4091-4113.
[31]Wang S,Shi T,Zhang L,et al.,Extended finite-time H∞control uncertain switched linear neural systems with time-varying delays,Neurocomputing,2015,152:377-387.
[32]Song J and He S,Finite-time H∞control for quasi-one-sided Lipschitz nonlinear systems,Neurocomputing,2015,149:1433-1439.
[33]Song J and He S,Robust finite-time H∞control for quasi-one-sided Lipschitz nonlinear systems via state feedback and output feedback,Journal of the Franklin Institute,2015,352:3250-3266.
[34]Lu R,Zhao S S,Wu Y,et al.,Finite-time bounded control for a class of stochastic nonlinear systems with randomly quantized measurements,Journal of the Franklin Institute,2016,353(17):4368-4383.
[35]Niamsup P and Phat V N,Robust finite-time control for linear time-varying delay systems with bounded control,Asian Journal of Control,2016,18(5):1-8.
[36]Niamsup P,Ratchgit K,and Phat V N,Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks,Neurocomputing,2015,160:281-286.
[37]Yan Z G,Zhang G,Wang J,et al.,State and output feedback finite-time guaranteed cost control of linear It o stochastic systems,Journal of Systems Science and Complexity,2015,28(4):813-829.
[38]Yan Z,Park J H,and Zhang W,Finite-time guaranteed cost control for It o stochastic Markovian jump systems with incomplete transition rates,International Journal of Robust and Nonlinear Control,2017,27:66-83.
[39]Cao X,Liu L,Fu Z,et al.,Guaranteed cost finite-time control for positive switched linear systems with time-varying delays,Journal of Control Science and Engineering,2017,Article ID 7051658,10 pages.
[40]Stojanovic S B,Further improvement in delay-dependent finite-time stability criteria for uncertain continuous-time systems with time-varying delays,IET Control Theory and Applications,2016,10(8):926-938.
[41]Kaczorek T,Stability of positive continuous-time linear systems with delays,Bulletin of the Polish Academy of Sciences:Technical Sciences,2009,57(4):395-398.
[42]Boyd S,Ghaoui L E,Feron E,et al.,Linear Matrix Inequalities in System and Control Theory,SIAM,Philadelphia,1994.
[43]Moon Y S,Park P G,and Kwon W H,Robust stabilization of uncertain input-delayed systems using reduction method,Automatica,2001,37:307-312.
[44]Yue D,Robust stabilization of uncertain systems with unknown input delay,Automatica,2004,40:331-336.
[45]De Oliveira M C,Geromel J C,and Bernusson J,Design of dynamic output feedback decentralized controllers via a separation procedure,International Journal of Control,2000,73(5):371-381.
[46]Thuan M V,Phat V N,and Trinh H,Dynamic output feedback guaranteed cost control for linear systems with interval time-varying delays in states and outputs,Applied Mathematics and Computation,2012,218:10697-10707.
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