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ON THE CONSTRUCTION OF GENERAL SOLUTION OF THE GENERALIZED SYLVESTER EQUATION

Year 2017, Volume: 7 Issue: 1, 1 - 6, 01.06.2017

Abstract

The problem of construction the general solution of the generalized matrix Sylvester equation is considered. Conditions of existence of solution of this equation are obtained and the algorithm for construction of this solution is given. For construction of the algorithm of this solution and the formulation of the condition of existence of this solution, the standard procedures of MATLAB package are used.

References

  • Afanas’ev,A.P., Dzyuba,S.M., Emelyanova,I.I., and Ramazanov,A.B., (2016), Optimal Control with feedback of some class of nonlinear systems via quadratic criteria, Appl. Comput.,Math., 15(1), pp.78- 87.
  • Aliev,F.A. and Larin,V.B., (1998), Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms. Amsterdam, Gordon and Breach Science Publishers, 261.
  • Aliev,F.A. and Larin,V.B., (2009), About Use of the Bass Relations for Solution of Matrix Equations, Appl. and Comput. Math., 8(2), pp.152-162.
  • Aliev,F.A., Larin,V.B., Velieva,N.I., and Gasimova,K.G., (2017), On Periodic Solution of Generalized Sylvestre Equations. Appl. Comput. Math., 16(1), pp.78-84.
  • Aliev,F.A. and Larin,V.B., (2015), Comment on ”Youla-Like Parametrizations Subject to QI Subspace Constrain” by Serban Sabau, Nuno C. Martins. Appl. Comput. Math., 14(3), pp.381-388.
  • Aliev,F.A., Ismailov,N.A., Haciyev,H., and Guliev,M.F., (2016), A method of Determine the Coeffi- cient of Hydraulic Resistance in Different Areas of Pump-Compressor Pipes. TWMS J. Pure Appl. Math., 7(2), pp.211-217.
  • Bischof,C., Datta,B.N., and Purkayastha,A., (1996), A Parallel Algorithm for Sylvester. Observer Equation, SIAM J. SCI. Comput. 17(3), pp.686-698.
  • Bryson,A.E. and Ho,Y.C., (1968), Applied Optimal Control. Optimization, Estimation and Control Watham Mass, 521p.
  • Chuiko,S.M., (2015), On the Solution of the Generalized Matrix Sylvester Equation. Chebyshev col- lection, 16(1), [In Russian].
  • Datta,B.N. and Sokolov,V., (2009), Quadratic Inverse Eigenvalue Problems, Active Vibration Control and Model Updating, Appl. Comput. Math., 8(2), pp.170-191.
  • Fedorov,F.M., (2015), On the Theory of Infinite Systems of Linear Algebraic Equations. TWMS J. Pure Appl. Math., 6(2), pp.202-212.
  • Jbilou,K.A., (2016), Survey of Krylov-Ased Methods for Model Reduction in Large-Scale MIMO Dynamical Systems. Appl. Comput. Math., 15(2), pp.117-148.
  • Larin,V.B., (2009), Control Problems for Wheeled Robotic Vehicles, Int. Appl. Mech., 45(4), pp.363- 388.
  • Larin,V.B., (2009), Solution of Matrix Equations in Problems of the Mechanics and Control, Int. Appl. Mech., 45(8), pp.847-872.
  • Larin,V.B., (2011), On Determination of Solution of Unilateral Quadratic Matrix Equation, J. Au- tomat Inf. Scien., 43(11), pp.8-17.
  • Lancaster,P., (1972), Theory of Matrix, Academic Press, New York-London, 280p.
  • Lee,R.C.K., (1964), Optimal Estimation, Identification and Control, Research Monograph No 28 The M.I.T. Press, Cambridge, Massachusetts, 176p.
  • Lin,Y. and Wei,Y., (2007), Condition Numbers of the Generalized Sylvester Equation, IEEE Trans. on Automat. Control., 52(12), pp.2380-2385.
  • Mahmudov,N.I. and Mckibben,M.A., (2016), On Approximately Controllable Systems (survey), Appl. Comput. Math., 15(3), pp.247-264.
  • Saeidian,J., Babolian,E., and Azizi,A., (2015), On a Homotopy Based Method for Solving Systems of Linear Equations, TWMS J. Pure Appl. Math., 6(1), pp.15-26.
  • Wu,A.G., Hu,J., and Duan,G.R., (2009), Solutions to the Matrix Equation AX − EXF = BY , Computers and Mathematics with Applications, 58, pp.1891-1900.
Year 2017, Volume: 7 Issue: 1, 1 - 6, 01.06.2017

Abstract

References

  • Afanas’ev,A.P., Dzyuba,S.M., Emelyanova,I.I., and Ramazanov,A.B., (2016), Optimal Control with feedback of some class of nonlinear systems via quadratic criteria, Appl. Comput.,Math., 15(1), pp.78- 87.
  • Aliev,F.A. and Larin,V.B., (1998), Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms. Amsterdam, Gordon and Breach Science Publishers, 261.
  • Aliev,F.A. and Larin,V.B., (2009), About Use of the Bass Relations for Solution of Matrix Equations, Appl. and Comput. Math., 8(2), pp.152-162.
  • Aliev,F.A., Larin,V.B., Velieva,N.I., and Gasimova,K.G., (2017), On Periodic Solution of Generalized Sylvestre Equations. Appl. Comput. Math., 16(1), pp.78-84.
  • Aliev,F.A. and Larin,V.B., (2015), Comment on ”Youla-Like Parametrizations Subject to QI Subspace Constrain” by Serban Sabau, Nuno C. Martins. Appl. Comput. Math., 14(3), pp.381-388.
  • Aliev,F.A., Ismailov,N.A., Haciyev,H., and Guliev,M.F., (2016), A method of Determine the Coeffi- cient of Hydraulic Resistance in Different Areas of Pump-Compressor Pipes. TWMS J. Pure Appl. Math., 7(2), pp.211-217.
  • Bischof,C., Datta,B.N., and Purkayastha,A., (1996), A Parallel Algorithm for Sylvester. Observer Equation, SIAM J. SCI. Comput. 17(3), pp.686-698.
  • Bryson,A.E. and Ho,Y.C., (1968), Applied Optimal Control. Optimization, Estimation and Control Watham Mass, 521p.
  • Chuiko,S.M., (2015), On the Solution of the Generalized Matrix Sylvester Equation. Chebyshev col- lection, 16(1), [In Russian].
  • Datta,B.N. and Sokolov,V., (2009), Quadratic Inverse Eigenvalue Problems, Active Vibration Control and Model Updating, Appl. Comput. Math., 8(2), pp.170-191.
  • Fedorov,F.M., (2015), On the Theory of Infinite Systems of Linear Algebraic Equations. TWMS J. Pure Appl. Math., 6(2), pp.202-212.
  • Jbilou,K.A., (2016), Survey of Krylov-Ased Methods for Model Reduction in Large-Scale MIMO Dynamical Systems. Appl. Comput. Math., 15(2), pp.117-148.
  • Larin,V.B., (2009), Control Problems for Wheeled Robotic Vehicles, Int. Appl. Mech., 45(4), pp.363- 388.
  • Larin,V.B., (2009), Solution of Matrix Equations in Problems of the Mechanics and Control, Int. Appl. Mech., 45(8), pp.847-872.
  • Larin,V.B., (2011), On Determination of Solution of Unilateral Quadratic Matrix Equation, J. Au- tomat Inf. Scien., 43(11), pp.8-17.
  • Lancaster,P., (1972), Theory of Matrix, Academic Press, New York-London, 280p.
  • Lee,R.C.K., (1964), Optimal Estimation, Identification and Control, Research Monograph No 28 The M.I.T. Press, Cambridge, Massachusetts, 176p.
  • Lin,Y. and Wei,Y., (2007), Condition Numbers of the Generalized Sylvester Equation, IEEE Trans. on Automat. Control., 52(12), pp.2380-2385.
  • Mahmudov,N.I. and Mckibben,M.A., (2016), On Approximately Controllable Systems (survey), Appl. Comput. Math., 15(3), pp.247-264.
  • Saeidian,J., Babolian,E., and Azizi,A., (2015), On a Homotopy Based Method for Solving Systems of Linear Equations, TWMS J. Pure Appl. Math., 6(1), pp.15-26.
  • Wu,A.G., Hu,J., and Duan,G.R., (2009), Solutions to the Matrix Equation AX − EXF = BY , Computers and Mathematics with Applications, 58, pp.1891-1900.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

F.a. Alıev This is me

V.b. Ların This is me

Publication Date June 1, 2017
Published in Issue Year 2017 Volume: 7 Issue: 1

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