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2D system analysis via dual problems and polynomial matrix inequalities
1. | Arzamas Polytechnic Institute, Alekseev Nizhny Novgorod State Technical University, 607220, Arzamas, Russian Federation |
References:
[1] |
P. Agathoklis, E. Jury and M. Mansour, Algebraic necessary and sufficient conditions for the stability of 2-D discrete systems, Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, 40 (1993), 251-258. |
[2] |
B. Anderson, P. Agathoklis, E. Jury and M. Mansour, Stability and the matrix Lyapunov equation for discrete 2-dimensional systems, Circuits and Systems, IEEE Transactions on, 33 (1986), 261-267.
doi: 10.1109/TCS.1986.1085912. |
[3] |
S. Boyd, L. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics, Society for Industrial and Applied Mathematics, 1994.
doi: 10.1137/1.9781611970777. |
[4] |
G. Chesi, LMI techniques for optimization over polynomials in control: A survey, Automatic Control, IEEE Transactions on, 55 (2010), 2500-2510.
doi: 10.1109/TAC.2010.2046926. |
[5] |
G. Chesi and R. Middleton, Necessary and sufficient LMI conditions for stability and performance analysis of 2-D mixed continuous-discrete-time systems, Automatic Control, IEEE Transactions on, 59 (2014), 996-1007.
doi: 10.1109/TAC.2014.2299353. |
[6] |
B. Cichy, P. Augusta, E. Rogers, K. Galkowski et al., On the control of distributed parameter systems using a multidimensional systems setting, Mechanical Syst. and Signal Processing, 22 (2008), 1566-1581. |
[7] |
G. Dullerud and R. D'Andrea, Distributed control of heterogeneous systems, Automatic Control, IEEE Transactions on, 49 (2004), 2113-2128.
doi: 10.1109/TAC.2004.838499. |
[8] |
D. Henrion and J.-B. Lasserre, Convergent relaxations of polynomial matrix inequalities and static output feedback, Automatic Control, IEEE Transactions on, 51 (2006), 192-202.
doi: 10.1109/TAC.2005.863494. |
[9] |
D. Henrion and J.-B. Lasserre, Detecting global optimality and extracting solutions in GloptiPoly, in Positive Polynomials in Control (eds. D. Henrion and A. Garulli), Springer Berlin Heidelberg, Berlin, Heidelberg, (2005), 293-310.
doi: 10.1007/10997703_15. |
[10] |
T. Hinamoto, 2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model, Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 40 (1993), 102-110. |
[11] |
V. Kamenetskiy and Y. Pyatnitskiy, An iterative method of Lyapunov function construction for differential inclusions, Systems & Control Letters, 8 (1987), 445-451.
doi: 10.1016/0167-6911(87)90085-5. |
[12] |
S. Knorn and R. Middleton, Stability of two-dimensional linear systems with singularities on the stability boundary using LMIs, Automatic Control, IEEE Transactions on, 58 (2013), 2579-2590.
doi: 10.1109/TAC.2013.2264852. |
[13] |
J.-B. Lasserre, Global optimization with polynomials and the problem of moments, SIAM Journal on Optimization, 11 (2001), 796-817.
doi: 10.1137/S1052623400366802. |
[14] |
Y. Li, M. Cantoni and E. Weyer, On water-level error propagation in controlled irrigation channels, in Proc. IEEE Conf. Decision Control and Eur. Control Conf., Seville, Spain, (2005), 2101-2106. |
[15] |
M. C. D. Oliveira, J. C. Geromel and J. Bernussou, Extended H2 and H∞ norm characterizations and controller parametrizations for discrete-time systems, International Journal of Control, 75 (2002), 666-679.
doi: 10.1080/00207170210140212. |
[16] |
W. Paszke, E. Rogers and K. Galkowski, H2/H∞ output information-based disturbance attenuation for differential linear repetitive processes, International Journal of Robust and Nonlinear Control, 21 (2011), 1981-1993.
doi: 10.1002/rnc.1672. |
[17] |
V. Pozdyayev, Atomic optimization. I. Search space transformation and one-dimensional problems, Automation and Remote Control, 74 (2013), 2069-2092.
doi: 10.1134/S0005117913120096. |
[18] |
V. Pozdyayev, Atomic optimization, II, Multidimensional problems and polynomial matrix inequalities, Automation and Remote Control, 75 (2014), 1155-1171.
doi: 10.1134/S0005117914060150. |
[19] |
V. Pozdyayev, Necessary conditions for 2D systems' stability, in Preprints, 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, (2015), 800-805. |
[20] |
R. Rabenstein and L. Trautmann, Towards a framework for continuous and discrete multidimensional systems, Int. J. of Applied Mathematics and Computer Science, 13 (2003), 73-86. |
[21] |
R. P. Roesser, A discrete state-space model for linear image processing, Automatic Control, IEEE Transactions on, 20 (1975), 1-10. |
[22] |
E. Rogers, K. Galkowski and D. Owens, Control systems theory and applications for linear repetitive processes, in Lecture Notes in Control and Information Sciences, vol. 349, Springer-Verlag, Berlin, 2007. |
[23] |
E. Rogers and D. Owens, Stability analysis for linear repetitive processes, in Lecture Notes in Control and Information Sciences, vol. 175, Springer-Verlag, Berlin, 1992.
doi: 10.1007/BFb0007165. |
[24] |
E. Rogers and D. Owens, Kronecker product based stability tests and performance bounds for a class of 2D continuous-discrete linear systems, Linear Algebra and its Applications, 353 (2002), 33-52.
doi: 10.1016/S0024-3795(02)00287-2. |
show all references
References:
[1] |
P. Agathoklis, E. Jury and M. Mansour, Algebraic necessary and sufficient conditions for the stability of 2-D discrete systems, Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, 40 (1993), 251-258. |
[2] |
B. Anderson, P. Agathoklis, E. Jury and M. Mansour, Stability and the matrix Lyapunov equation for discrete 2-dimensional systems, Circuits and Systems, IEEE Transactions on, 33 (1986), 261-267.
doi: 10.1109/TCS.1986.1085912. |
[3] |
S. Boyd, L. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics, Society for Industrial and Applied Mathematics, 1994.
doi: 10.1137/1.9781611970777. |
[4] |
G. Chesi, LMI techniques for optimization over polynomials in control: A survey, Automatic Control, IEEE Transactions on, 55 (2010), 2500-2510.
doi: 10.1109/TAC.2010.2046926. |
[5] |
G. Chesi and R. Middleton, Necessary and sufficient LMI conditions for stability and performance analysis of 2-D mixed continuous-discrete-time systems, Automatic Control, IEEE Transactions on, 59 (2014), 996-1007.
doi: 10.1109/TAC.2014.2299353. |
[6] |
B. Cichy, P. Augusta, E. Rogers, K. Galkowski et al., On the control of distributed parameter systems using a multidimensional systems setting, Mechanical Syst. and Signal Processing, 22 (2008), 1566-1581. |
[7] |
G. Dullerud and R. D'Andrea, Distributed control of heterogeneous systems, Automatic Control, IEEE Transactions on, 49 (2004), 2113-2128.
doi: 10.1109/TAC.2004.838499. |
[8] |
D. Henrion and J.-B. Lasserre, Convergent relaxations of polynomial matrix inequalities and static output feedback, Automatic Control, IEEE Transactions on, 51 (2006), 192-202.
doi: 10.1109/TAC.2005.863494. |
[9] |
D. Henrion and J.-B. Lasserre, Detecting global optimality and extracting solutions in GloptiPoly, in Positive Polynomials in Control (eds. D. Henrion and A. Garulli), Springer Berlin Heidelberg, Berlin, Heidelberg, (2005), 293-310.
doi: 10.1007/10997703_15. |
[10] |
T. Hinamoto, 2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model, Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 40 (1993), 102-110. |
[11] |
V. Kamenetskiy and Y. Pyatnitskiy, An iterative method of Lyapunov function construction for differential inclusions, Systems & Control Letters, 8 (1987), 445-451.
doi: 10.1016/0167-6911(87)90085-5. |
[12] |
S. Knorn and R. Middleton, Stability of two-dimensional linear systems with singularities on the stability boundary using LMIs, Automatic Control, IEEE Transactions on, 58 (2013), 2579-2590.
doi: 10.1109/TAC.2013.2264852. |
[13] |
J.-B. Lasserre, Global optimization with polynomials and the problem of moments, SIAM Journal on Optimization, 11 (2001), 796-817.
doi: 10.1137/S1052623400366802. |
[14] |
Y. Li, M. Cantoni and E. Weyer, On water-level error propagation in controlled irrigation channels, in Proc. IEEE Conf. Decision Control and Eur. Control Conf., Seville, Spain, (2005), 2101-2106. |
[15] |
M. C. D. Oliveira, J. C. Geromel and J. Bernussou, Extended H2 and H∞ norm characterizations and controller parametrizations for discrete-time systems, International Journal of Control, 75 (2002), 666-679.
doi: 10.1080/00207170210140212. |
[16] |
W. Paszke, E. Rogers and K. Galkowski, H2/H∞ output information-based disturbance attenuation for differential linear repetitive processes, International Journal of Robust and Nonlinear Control, 21 (2011), 1981-1993.
doi: 10.1002/rnc.1672. |
[17] |
V. Pozdyayev, Atomic optimization. I. Search space transformation and one-dimensional problems, Automation and Remote Control, 74 (2013), 2069-2092.
doi: 10.1134/S0005117913120096. |
[18] |
V. Pozdyayev, Atomic optimization, II, Multidimensional problems and polynomial matrix inequalities, Automation and Remote Control, 75 (2014), 1155-1171.
doi: 10.1134/S0005117914060150. |
[19] |
V. Pozdyayev, Necessary conditions for 2D systems' stability, in Preprints, 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, (2015), 800-805. |
[20] |
R. Rabenstein and L. Trautmann, Towards a framework for continuous and discrete multidimensional systems, Int. J. of Applied Mathematics and Computer Science, 13 (2003), 73-86. |
[21] |
R. P. Roesser, A discrete state-space model for linear image processing, Automatic Control, IEEE Transactions on, 20 (1975), 1-10. |
[22] |
E. Rogers, K. Galkowski and D. Owens, Control systems theory and applications for linear repetitive processes, in Lecture Notes in Control and Information Sciences, vol. 349, Springer-Verlag, Berlin, 2007. |
[23] |
E. Rogers and D. Owens, Stability analysis for linear repetitive processes, in Lecture Notes in Control and Information Sciences, vol. 175, Springer-Verlag, Berlin, 1992.
doi: 10.1007/BFb0007165. |
[24] |
E. Rogers and D. Owens, Kronecker product based stability tests and performance bounds for a class of 2D continuous-discrete linear systems, Linear Algebra and its Applications, 353 (2002), 33-52.
doi: 10.1016/S0024-3795(02)00287-2. |
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