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2019 | OriginalPaper | Chapter

3. Discrete-Time Systems with Switching

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Abstract

In the present chapter we set out a general approach to stability analysis problem for a set of trajectories of difference equations with uncertain parameter values.

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Literature
2.
go back to reference Aleksandrov, A.Yu., Platonov, A.V.: Aggregation and stability analysis of nonlinear complex systems. J. Math. Anal. Appl. 342(2), 989–1002 (2008)MathSciNetMATHCrossRef Aleksandrov, A.Yu., Platonov, A.V.: Aggregation and stability analysis of nonlinear complex systems. J. Math. Anal. Appl. 342(2), 989–1002 (2008)MathSciNetMATHCrossRef
3.
go back to reference Aleksandrov, A.Yu., Platonov, A.V.: Conditions of ultimate boundedness of solutions for a class of nonlinear systems. Nonlinear Dyn. Syst. Theory 8(2), 109–122 (2008)MathSciNetMATH Aleksandrov, A.Yu., Platonov, A.V.: Conditions of ultimate boundedness of solutions for a class of nonlinear systems. Nonlinear Dyn. Syst. Theory 8(2), 109–122 (2008)MathSciNetMATH
4.
go back to reference Aleksandrov, A.Yu., Zhabko, A.P.: Preservation of stability under discretization of systems of ordinary differential equations. Sib. Math. J. 51(3), 383–395 (2010)MathSciNetMATHCrossRef Aleksandrov, A.Yu., Zhabko, A.P.: Preservation of stability under discretization of systems of ordinary differential equations. Sib. Math. J. 51(3), 383–395 (2010)MathSciNetMATHCrossRef
5.
go back to reference Aleksandrov, A.Yu., Martynyuk, A.A., Platonov, A.V.: Analysis of a set of nonlinear dynamics trajectories: stability of difference equations. J. Math. Anal. Appl. 421(1), 105–117 (2015)MathSciNetMATHCrossRef Aleksandrov, A.Yu., Martynyuk, A.A., Platonov, A.V.: Analysis of a set of nonlinear dynamics trajectories: stability of difference equations. J. Math. Anal. Appl. 421(1), 105–117 (2015)MathSciNetMATHCrossRef
6.
go back to reference Aleksandrov, A.Yu., Martynyuk, A.A., Platonov, A.V.: Stability analysis of nonlinear switched difference systems via the comparison method. Pan Am. Math. J. 25(2), 71–88 (2015)MathSciNetMATH Aleksandrov, A.Yu., Martynyuk, A.A., Platonov, A.V.: Stability analysis of nonlinear switched difference systems via the comparison method. Pan Am. Math. J. 25(2), 71–88 (2015)MathSciNetMATH
7.
go back to reference Aleksandrov, A.Yu., Martynyuk, A.A., Platonov, A.V.: Dwell time stability analysis for nonlinear switched difference systems. Nonlinear Dyn. Syst. Theory 16(3), 221–234 (2016)MathSciNetMATH Aleksandrov, A.Yu., Martynyuk, A.A., Platonov, A.V.: Dwell time stability analysis for nonlinear switched difference systems. Nonlinear Dyn. Syst. Theory 16(3), 221–234 (2016)MathSciNetMATH
24.
51.
go back to reference Lakshmikantham, V., Leela, S., Martynyuk, A.A.: Stability Analysis of Nonlinear Systems, 2nd edn. Springer, Basel (2015)MATHCrossRef Lakshmikantham, V., Leela, S., Martynyuk, A.A.: Stability Analysis of Nonlinear Systems, 2nd edn. Springer, Basel (2015)MATHCrossRef
52.
55.
go back to reference Liberzon, D., Morse, A.S.: Basic problems in stability and design of switched systems. IEEE Contr. Syst. Mag. 19(15), 59–70 (1999)MATH Liberzon, D., Morse, A.S.: Basic problems in stability and design of switched systems. IEEE Contr. Syst. Mag. 19(15), 59–70 (1999)MATH
57.
go back to reference Lukyanova, T.A., Martynyuk, A.A.: Robust stability: three approaches for discrete-time systems. Nonlinear Dyn. Syst. Theory 2(1), 45–55 (2002)MathSciNetMATH Lukyanova, T.A., Martynyuk, A.A.: Robust stability: three approaches for discrete-time systems. Nonlinear Dyn. Syst. Theory 2(1), 45–55 (2002)MathSciNetMATH
66.
go back to reference Martynyuk, A.A.: Qualitative Methods in Nonlinear Dynamics. Novel Approaches to Liapunov’s Matrix Function. Marcel Dekker, New York (2002) Martynyuk, A.A.: Qualitative Methods in Nonlinear Dynamics. Novel Approaches to Liapunov’s Matrix Function. Marcel Dekker, New York (2002)
68.
go back to reference Martynyuk, A.A.: On the theory of Lyapunov’s direct method. Dokl. Math. 73(4), 376–379 (2006)MATHCrossRef Martynyuk, A.A.: On the theory of Lyapunov’s direct method. Dokl. Math. 73(4), 376–379 (2006)MATHCrossRef
69.
go back to reference Martynyuk, A.A.: Stability of Motion. The Role of Multicomponent Liapunov’s Functions. Cambridge Scientific Publishers, Cambridge (2007) Martynyuk, A.A.: Stability of Motion. The Role of Multicomponent Liapunov’s Functions. Cambridge Scientific Publishers, Cambridge (2007)
72.
go back to reference Martynyuk, A.A.: Asymptotic stability criterion for nonlinear monotonic systems and its applications (Review). Int. Appl. Mech. 47(5), 475–534 (2011)MathSciNetMATHCrossRef Martynyuk, A.A.: Asymptotic stability criterion for nonlinear monotonic systems and its applications (Review). Int. Appl. Mech. 47(5), 475–534 (2011)MathSciNetMATHCrossRef
76.
go back to reference Martynyuk, A.A.: On the stability of trajectories of the set of difference equations. Dokl. NAS Ukr. 5, 65–69 (2014)MathSciNetMATH Martynyuk, A.A.: On the stability of trajectories of the set of difference equations. Dokl. NAS Ukr. 5, 65–69 (2014)MathSciNetMATH
82.
go back to reference Martynyuk, A.A., Obolenskij, A.Yu.: Stability of solutions of autonomous Wazewskij systems. Differ. Equ. 16(8), 1392–1407 (1980) Martynyuk, A.A., Obolenskij, A.Yu.: Stability of solutions of autonomous Wazewskij systems. Differ. Equ. 16(8), 1392–1407 (1980)
89.
go back to reference Martynyuk, A.A., Miladzhanov, V.G.: Stability Analysis of Nonlinear Systems Under Structural Perturbations. Cambridge Scientific Publishers, Cambridge (2014)MATH Martynyuk, A.A., Miladzhanov, V.G.: Stability Analysis of Nonlinear Systems Under Structural Perturbations. Cambridge Scientific Publishers, Cambridge (2014)MATH
116.
go back to reference Vassilyev, S.N., Kosov, A.A., Malikov, A.I.: Stability analysis of nonlinear switched systems via reduction method. In: Proceedings of the 18th IFAC World Congress, Milano, vol. 18, Part 1, pp. 5718–5723 (2011) Vassilyev, S.N., Kosov, A.A., Malikov, A.I.: Stability analysis of nonlinear switched systems via reduction method. In: Proceedings of the 18th IFAC World Congress, Milano, vol. 18, Part 1, pp. 5718–5723 (2011)
124.
go back to reference Zubov, V.I.: Mathematical Methods of Investigations of Systems Automatical Control. Sudpromgiz, Leningrad (1959) Zubov, V.I.: Mathematical Methods of Investigations of Systems Automatical Control. Sudpromgiz, Leningrad (1959)
Metadata
Title
Discrete-Time Systems with Switching
Author
Anatoly A. Martynyuk
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-07644-3_3