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The continuous matching of two stable linear systems can be unstable
1. | Departamento Matemática Aplicada II, Escuela Técnica Superior de Ingenieros. Universidad de Sevilla, Camino de los Descubrimientos s/n, Sevilla 41092, Spain, Spain, Spain, Spain |
[1] |
Victoriano Carmona, Emilio Freire, Soledad Fernández-García. Periodic orbits and invariant cones in three-dimensional piecewise linear systems. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 59-72. doi: 10.3934/dcds.2015.35.59 |
[2] |
Miguel Ângelo De Sousa Mendes. Quasi-invariant attractors of piecewise isometric systems. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 323-338. doi: 10.3934/dcds.2003.9.323 |
[3] |
Christian Pötzsche, Stefan Siegmund, Fabian Wirth. A spectral characterization of exponential stability for linear time-invariant systems on time scales. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1223-1241. doi: 10.3934/dcds.2003.9.1223 |
[4] |
Jaume Llibre, Lucyjane de A. S. Menezes. On the limit cycles of a class of discontinuous piecewise linear differential systems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1835-1858. doi: 10.3934/dcdsb.2020005 |
[5] |
Victoriano Carmona, Soledad Fernández-García, Antonio E. Teruel. Saddle-node of limit cycles in planar piecewise linear systems and applications. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5275-5299. doi: 10.3934/dcds.2019215 |
[6] |
Song-Mei Huan, Xiao-Song Yang. On the number of limit cycles in general planar piecewise linear systems. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2147-2164. doi: 10.3934/dcds.2012.32.2147 |
[7] |
Rafel Prohens, Antonio E. Teruel. Canard trajectories in 3D piecewise linear systems. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4595-4611. doi: 10.3934/dcds.2013.33.4595 |
[8] |
Shimin Li, Jaume Llibre. On the limit cycles of planar discontinuous piecewise linear differential systems with a unique equilibrium. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 5885-5901. doi: 10.3934/dcdsb.2019111 |
[9] |
Rovella Alvaro, Vilamajó Francesc, Romero Neptalí. Invariant manifolds for delay endomorphisms. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 35-50. doi: 10.3934/dcds.2001.7.35 |
[10] |
Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3837-3849. doi: 10.3934/dcdss.2020444 |
[11] |
Claudio Buzzi, Claudio Pessoa, Joan Torregrosa. Piecewise linear perturbations of a linear center. Discrete and Continuous Dynamical Systems, 2013, 33 (9) : 3915-3936. doi: 10.3934/dcds.2013.33.3915 |
[12] |
Alexander Pimenov, Dmitrii I. Rachinskii. Linear stability analysis of systems with Preisach memory. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 997-1018. doi: 10.3934/dcdsb.2009.11.997 |
[13] |
Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233 |
[14] |
Jaume Llibre. Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022034 |
[15] |
Ciprian D. Coman. Dissipative effects in piecewise linear dynamics. Discrete and Continuous Dynamical Systems - B, 2003, 3 (2) : 163-177. doi: 10.3934/dcdsb.2003.3.163 |
[16] |
Siniša Slijepčević. Stability of invariant measures. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1345-1363. doi: 10.3934/dcds.2009.24.1345 |
[17] |
Byungik Kahng, Miguel Mendes. The characterization of maximal invariant sets of non-linear discrete-time control dynamical systems. Conference Publications, 2013, 2013 (special) : 393-406. doi: 10.3934/proc.2013.2013.393 |
[18] |
Elimhan N. Mahmudov. Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 353-371. doi: 10.3934/naco.2021010 |
[19] |
José F. Alves, Davide Azevedo. Statistical properties of diffeomorphisms with weak invariant manifolds. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 1-41. doi: 10.3934/dcds.2016.36.1 |
[20] |
George Osipenko. Indestructibility of invariant locally non-unique manifolds. Discrete and Continuous Dynamical Systems, 1996, 2 (2) : 203-219. doi: 10.3934/dcds.1996.2.203 |
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