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Języki publikacji
Abstrakty
We investigate a scalar characteristic exponential polynomial with complex coefficients associated with a first order scalar differential-difference equation. Our analysis provides necessary and sufficient conditions for allocation of the roots in the complex open left half-plane what guarantees asymptotic stability of the differential-difference equation. The conditions are expressed explicitly in terms of complex coefficients of the characteristic exponential polynomial, what makes them easy to use in applications. We show examples including those for retarded PDEs in an abstract formulation.
Czasopismo
Rocznik
Tom
Strony
607--629
Opis fizyczny
Bibliogr. 18 poz., rys., wzory
Twórcy
autor
- Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków
autor
- Department of Automatic Control and Robotics, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice
Bibliografia
- [1] V.K. Barwell: Special stability problems for functional differential equations. BIT BIT Numerical Mathematics, 15 (1975), 130-135. DOI: 10.1007/BF01932685.
- [2] D. Breda: On characteristic roots and stability charts of delay differentia equations. International Journal of Robust and Nonlinear Control, 22(8), (2012), 892-917. DOI: 10.1002/rnc.1734.
- [3] B. Cahlon and D. Schmidt: On stability of a frst-order complex delay differential equation. Nonlinear Analysis: Real World Applications, 3(3), (2002), 413-429. DOI: 10.1016/S1468-1218(01)00039-6.
- [4] K.L. Cooke and Z. Grossman: Discrete delay, distributed delay and stability switches. Journal of Mathematical Analysis and Applications, 86(2), (1982), 592-627. DOI: 10.1016/0022-247X(82)90243-8.
- [5] O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel and H.-O. Walther: Delay Equations Functional-, Complex-, and Nonlinear Analysis, Applied Mathematical Sciences, 110 Springer-Verlag, New York, 1995. DOI: 10.1007/978-1-4612-4206-2.
- [6] N.D. Hayes: Roots of the transcendental equation associated with a certain difference-differential equation. Journal of the London Mathematical Society s1-25(3), (1950), 226-232. DOI: 10.1112/jlms/s1-25.3.226.
- [7] R. Kapica, J.R. Partington and R. Zawiski: Admissibility of retarded diagonal systems with one dimensional input space. Mathematics of Control, Signals, and Systems, 35 (2023), 433-465. DOI: 10.1007/s00498-023-00345-6.
- [8] H. Matsunaga: Delay-dependent and delay-independent stability criteria for a delay differential system. Proceedings of the American Mathematical Society, 136 (2008), 4305-4312. DOI: 10.1090/S0002-9939-08-09396-9.
- [9] T.S. Motzkin and O. Taussky: Pairs of matrices with property L. Transactions of the American Mathematical Society, 73(1), (1952), 108-114. DOI: 10.2307/1990825.
- [10] J. Nishiguchi: On parameter dependence of exponential stability of equilibrium solutions in differential equations with a single constant delay. Discrete and Continuous Dynamical Systems, 36(10), (2016), 5657-5679. DOI: 10.3934/dcds.2016048.
- [11] V.W. Noonburg: Roots of a transcendental equation associated with a system of differential-difference equations. SIAM Journal of Applied Mathematics, 17(1), (1969), 198-205. DOI: 10.1137/0117019.
- [12] J.R. Partington: Linear Operators and Linear Systems: An Analytical Approach to Control Theory. London Mathematical Society Student Texts, 60 Cambridge University Press, Cambridge, UK, 2004. DOI: 10.1017/CBO9780511616693.
- [13] J.R. Partington and R. Zawiski: Admissibility of state delay diagonal systems with one-dimensional input space. Complex Analysis and Operator Theory, 13 (2019), 2463-2485. DOI: 10.1007/s11785-019-00910-5.
- [14] G. Stépán: Retarded Dynamical Systems: Stability and Characteristic Functions. Longman Scientific and Technical, Harlow, 1989.
- [15] M. Tucsnak and G. Weiss: Observation and Control for Operator Semi-groups. Birkhäuser Verlag AG, Basel, 2009, DOI: 10.1007/978-3-7643-8994-9.
- [16] K. Walton and J.E. Marshall: Direct method for TDS stability analysis. IEE Proceedings D - Control Theory and Applications, 134(2), (1987), 101-107, DOI: 10.1049/ip-d.1987.0018.
- [17] J. Wei and C. Zhang: Stability analysis in a first-order complex differentia equations with delay. Nonlinear Analysis, 59(5), (2004), 657-671. DOI: 10.1016/j.na.2004.07.027.
- [18] W. Michiels and S.-I. Niculescu: Stability, Control, and Computation for Time-Delay Systems. SIAM, Philadelphia, 2014, DOI: 10.1137/1.9781611973631.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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