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Some methods of construction of a common Lyapunov solution to a finite set of complex systems. (English) Zbl 1368.15018

Summary: In this work, two methods of determining a common Lyapunov solution for a finite number of complex matrices are proposed. The first one is an extension to the complex case of T. Büyükköroğlu’s result [J. Comput. Appl. Math. 236, No. 15, 3647–3653 (2012; Zbl 1242.93120)] dedicated to real matrices of order three whereas the second one, extending and completing a very recent paper of M. Gumus and J. Xu [Linear Algebra Appl. 507, 32–50 (2016; Zbl 1382.93029)], can be applied to a finite set of complex matrices of arbitrary order. As special cases, some known results as well as new ones concerning the common Lyapunov solution problem for complex triangular systems are derived. Numerical examples are presented to illustrate and to compare the results.

MSC:

15A45 Miscellaneous inequalities involving matrices
15B48 Positive matrices and their generalizations; cones of matrices
34D20 Stability of solutions to ordinary differential equations
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D09 Robust stability
93D30 Lyapunov and storage functions
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