Approximating the Spectral Abscissa for Switched Linear Systems via Coordinate Transformations
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Liberzon D and Morse A S, Basic problems in stability and design of switched systems, IEEE Control Systems Magazine, 1999, 19(5): 59–70.
Hespanha J P, Uniform stability of switched linear systems: Extensions of LaSalle’s invariance principle, IEEE Trans. on Automatic Control, 2004, 49(4): 470–482.
Shorten R, Wirth F, Mason O, Wulff K, and King C, Stability criteria for switched and hybrid systems, SIAM Review, 2007, 49(4): 545–592.
Lin H and Antsaklis P J, Stability and stabilizability of switched linear systems: A survey of recent results, IEEE Trans. on Automatic Control, 2009, 54(2): 308–322.
Zhao X D, Zhang L X, Shi P, and Liu M, Stability and stabilization of switched linear systems with mode-dependent average dwell time, IEEE Trans. on Automatic Control, 2012, 57(7): 1809–1815.
Zhao X D, Yin S, Li H Y, and Niu B, Switching stabilization for a class of slowly switched systems, IEEE Trans. on Automatic Control, 2014, 60(1): 221–226.
Molchanov A P and Pyatnitskiy Y S, Criteria of asymptotic stability of differential and difference inclusions encountered in control theory, Systems & Control Letters, 1989, 13(1): 59–64.
Narendra K S and Balakrishnan J, A common Lyapunov function for stable LTI systems with commuting A-matrices, IEEE Trans. on Automatic Control, 1994, 39(12): 2469–2471.
Zhai G S, Liu D R, Imae J, and Kobayashi T, Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems, IEEE Trans. on Circuits and Systems-II, 2006, 53(2): 152–156.
Dayawansa W P and Martin C F, A converse Lyapunov theorem for a class of dynamical systems which undergo switching, IEEE Trans. on Automatic Control, 1999, 44(4): 751–760.
Mason P, Boscain U, and Chitour Y, Common polynomial Lyapunov functions for linear switched systems, SIAM Journal on Control and Optimization, 2006, 45: 226–245.
Protasov V Y and Jungers R M, Is switching systems stability harder for continuous time systems? 52nd IEEE Conference on Decision and Control, Firenze, 2013, 704–709.
Barabanov N E, Ways to compute the Lyapunov index for differential nesting, Automation and Remote Control, 1989, 50(4): 475–479.
Sun Z D, Matrix measure approach for stability of switched linear systems, 7th IFAC Symposium Nonlinear Control System, Pretoria, 2007, 557–560.
Xiong J D and Sun Z D, Approximation of extreme measure for switched linear systems, 9th IEEE International Conference on Control and Automation, Santiago, 2011, 722–725.
Blanchini F, The gain scheduling and the robust state feedback stabilization problems, IEEE Trans. on Automatic Control, 2000, 45(11): 2061–2070.
Lin M L and Sun Z D, Calculation of the least ℒ 1 measure for switched linear systems via similarity transformation, 9th Asian Control Conference, Istanbul, 2013, 1–6.
Parrilo P A and Jadbabaie A, Approximation of the joint spectral radius using sum of squares, Linear Algebra and Its Applications, 2008, 428(10): 2385–2402.
Chitour Y, Mason P, and Sigalotti M, On the marginal instability of linear switched systems, 49th IEEE Conference on Decision and Control, Atlanta, 2010, 747–757.
Gurvits L, Stability of discrete linear inclusions, Linear Algebra and Its Applications, 1995, 231: 47–85.
Shih M H, Wu J W, and Pang C T, Asymptotic stability and generalized Gelfand spectral radius formula, Linear Algebra and Its Applications, 1997, 252: 61–70.
Margaliot M and Langholz G, Necessary and sufficient conditions for absolute stability: The case of second-order systems, IEEE Trans. on Circuits and Systems-I, 2003, 50(2): 227–234.
Margaliot M and Yfoulis C, Absolute stability of third-order systems: A numerical algorithm, Automatica, 2006, 42: 1705–1711.
Xiong J D and Sun Z D, Accurate estimation of the largest divergence rate for a class of the 3rd-order switched linear systems, Journal of Control & Applications, 2013, 11(3): 513–516.
Xie L, Shishkin S, and Fu M Y, Piecewise Lyapunov functions for robust stability of linear timevarying systems, Systems & Control Letters, 1997, 31: 165–171.