Explicit Iterative Algorithms for Continuous Coupled Lyapunov Matrix Equations
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- 英文论文题名：Explicit Iterative Algorithms for Continuous Coupled Lyapunov Matrix Equations
- 论文作者：Wan-Qi Wu ; Hui-Jie Sun ; Hang-Qing Lin ; Ying Zhang
- 英文论文作者：Wan-Qi Wu ; Hui-Jie Sun ; Hang-Qing Lin ; Ying Zhang ; Harbin Institute of Technology Shenzhen Graduate School
- 年：2017
- 作者机构：Harbin Institute of Technology Shenzhen Graduate School;
- 英文论文关键词：Iterative Algorithm ; Coupled Lyapunov Matrix Equation ; Markovian Jump Linear Systems
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O241.6
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：4
- 文件大小：212k
- 原文格式：D
- 会议级别：全国
摘要
Two explicit iterative algorithms are developed in this paper for solving continuous coupled Lyapunov matrix equations. By introducing a tunable parameter, the considered matrix equations are transformed into the Kalman-Yakubovich matrix equations. Further, based on the obtained equations, an explicit iterative algorithm is constructed to solve the coupled Lyapunov matrix equations. In addition, by using the latest estimation an improved iterative algorithm is proposed. Some convergence results are obtained for the presented improved iterative algorithm. It is shown that the convergence performance of the proposed algorithms can be significantly improved if the tunable parameter can be properly chosen. Finally, a numerical example is given to show the merit of the presented algorithms.
Two explicit iterative algorithms are developed in this paper for solving continuous coupled Lyapunov matrix equations. By introducing a tunable parameter, the considered matrix equations are transformed into the Kalman-Yakubovich matrix equations. Further, based on the obtained equations, an explicit iterative algorithm is constructed to solve the coupled Lyapunov matrix equations. In addition, by using the latest estimation an improved iterative algorithm is proposed. Some convergence results are obtained for the presented improved iterative algorithm. It is shown that the convergence performance of the proposed algorithms can be significantly improved if the tunable parameter can be properly chosen. Finally, a numerical example is given to show the merit of the presented algorithms.
Two explicit iterative algorithms are developed in this paper for solving continuous coupled Lyapunov matrix equations. By introducing a tunable parameter, the considered matrix equations are transformed into the Kalman-Yakubovich matrix equations. Further, based on the obtained equations, an explicit iterative algorithm is constructed to solve the coupled Lyapunov matrix equations. In addition, by using the latest estimation an improved iterative algorithm is proposed. Some convergence results are obtained for the presented improved iterative algorithm. It is shown that the convergence performance of the proposed algorithms can be significantly improved if the tunable parameter can be properly chosen. Finally, a numerical example is given to show the merit of the presented algorithms.
引文
[1]M.Mariton,Jump linear systems in automatic control[M],New York:M.Dekker,1990.
[2]F.Xiangbo,et al.Stochastic stability properties of jump linear systems[J],IEEE Transactions on Automatic Control1992,37(1):38-53.
[3]L.Jodar,and M.Mariton.Explicit solutions for a system of coupled Lyapunov differential matrix equations[J],Proceedings of the Edinburgh Mathematical Society(Series 2)1987,30(03):427-434.
[4]L.Zhao-Yan,et al,Positive operator based iterative algorithms for solving Lyapunov equations for Ito stochastic systems with Markovian jumps[J],Applied Mathematics and Computation 2011,217(21):8179-8195.
[5]I.Borno,and G.Zoran,Parallel algorithms for optimal control of weakly coupled and singularly perturbed jump linear systems[J].Automatica,1995,31(7):985-988.
[6]I.Borno,Parallel computation of the solutions of coupled algebraic Lyapunov equations[J],Automatica 1995,31(9):1345-1347.
[7]Z.Bin,D.Guang-Ren,and L.Zhao-Yan,Gradient based iterative algorithm for solving coupled matrix equations[J],Systems&Control Letters 2009,58(5):327-333.
[8]W.Ai-Guo,and D.Guang-Ren,New iterative algorithms for solving coupled Markovian jump Lyapunov equations[J],IEEE Transactions on Automatic Control 2015,60(1):289-294.
[9]Q.Yang-Yang,and P.Wen-Jie,An implicit sequential algorithm for solving coupled Lyapunov equations of continuoustime Markovian jump systems[J],Automatica 2015,60:245-250.
[10]L.V.Kantorovich,V.Leonid,and P.A.Gleb,Functional analysis in normed spaces[J],1964.
[11]Z.Bin,D.Guang-Ren,and L.Zhao-Yan.Gradient based iterative algorithm for solving coupled matrix equations[J],Systems&Control Letters 2009,58(5):327-333.
[2]F.Xiangbo,et al.Stochastic stability properties of jump linear systems[J],IEEE Transactions on Automatic Control1992,37(1):38-53.
[3]L.Jodar,and M.Mariton.Explicit solutions for a system of coupled Lyapunov differential matrix equations[J],Proceedings of the Edinburgh Mathematical Society(Series 2)1987,30(03):427-434.
[4]L.Zhao-Yan,et al,Positive operator based iterative algorithms for solving Lyapunov equations for Ito stochastic systems with Markovian jumps[J],Applied Mathematics and Computation 2011,217(21):8179-8195.
[5]I.Borno,and G.Zoran,Parallel algorithms for optimal control of weakly coupled and singularly perturbed jump linear systems[J].Automatica,1995,31(7):985-988.
[6]I.Borno,Parallel computation of the solutions of coupled algebraic Lyapunov equations[J],Automatica 1995,31(9):1345-1347.
[7]Z.Bin,D.Guang-Ren,and L.Zhao-Yan,Gradient based iterative algorithm for solving coupled matrix equations[J],Systems&Control Letters 2009,58(5):327-333.
[8]W.Ai-Guo,and D.Guang-Ren,New iterative algorithms for solving coupled Markovian jump Lyapunov equations[J],IEEE Transactions on Automatic Control 2015,60(1):289-294.
[9]Q.Yang-Yang,and P.Wen-Jie,An implicit sequential algorithm for solving coupled Lyapunov equations of continuoustime Markovian jump systems[J],Automatica 2015,60:245-250.
[10]L.V.Kantorovich,V.Leonid,and P.A.Gleb,Functional analysis in normed spaces[J],1964.
[11]Z.Bin,D.Guang-Ren,and L.Zhao-Yan.Gradient based iterative algorithm for solving coupled matrix equations[J],Systems&Control Letters 2009,58(5):327-333.