On the Lyapunov stability theory for impulsive dynamical systems
Keywords
Lyapunov functions, stability, dynamical systems, impulsesAbstract
In this work, we establish necessary and sufficient conditions for the uniform and orbital stability of a special class of sets on impulsive dynamical systems. The results are achieved by means of Lyapunov functions.References
R. Ambrosino, F. Calabrese, C. Cosentino and G. De Tommasi, Sufficient conditions for finite-time stability of impulsive dynamical systems, IEEE Trans. Autom. Control 54 (2009), 861–865.
E.M. Bonotto, M.C. Bortolan, A.N. Carvalho and R. Czaja, Global attractors for impulsive dynamical systems — a precompact approach, J. Differential Equations 259 (2015), 2602–2625.
E.M. Bonotto and J. Costa Ferreira, Dissipativity in impulsive systems via Lyapunov functions, Math. Nachr. 289 (2016), 213–231.
E.M. Bonotto and D.P. Demuner, Autonomous dissipative semidynamical systems with impulses, Topol. Methods Nonlinear Anal. 41 (2013), no. 1, 1–38.
E.M. Bonotto, L.P. Gimenes and G.M. Souto, On Jack Hale’s problem for impulsive systems, J. Differential Equations 259 (2015), no. 2, 642–665.
E.M. Bonotto, L.P. Gimenes and G.M. Souto, Asymptotically almost periodic motions in impulsive semidynamical systems, Topol. Methods Nonlinear Anal. 49 (2017), 133–163.
E.M. Bonotto and N.G. Grulha Jr., Lyapunov stability of closed sets in impulsive semidynamical systems, Electron. J. Differential Equations 78 (2010), 1–18.
K. Ciesielski, On semicontinuity in impulsive dynamical systems, Bull. Polish Acad. Sci. Math., 52 (2004), 71–80.
K. Ciesielski, On stability in impulsive dynamical systems, Bull. Polish Acad. Sci. Math., 52 (2004), 81–91.
K. Ciesielski, On time reparametrization and isomorphisms of impulsive dynamical system, Ann. Polon. Math., 84 (2004), 1–25.
J. Cortés, Discontinuous dynamical systems: a tutorial on solutions, nonsmooth analysis, and stability, IEEE Control Syst. Mag. 28 (2008), no. 3, 36–73.
M.H.A. Davis, X. Guo and Gouliang Wu, Impulsive control of multidimentional jump diffusions, SIAM J. Control Optim. 48 (2010), 5276–5293.
C. Ding, Lyapunov quasi-stable trajectories, Fund. Math. 220 (2013), 139–154.
A. El-Gohary and A.S. Al-Ruzaiza, Chaos and adaptive control in two prey, one predator system with nonlinear feedback, Chaos Solitons Fractals 34 (2007), 443–453.
H. Hu, K. Wang and D. Wu, Permanence and global stability for nonautonomous Nspecies Lotka–Volterra competitive system with impulses and infinite delays, J. Math. Anal. Appl. 377 (2011), no. 1, 145–160.
S.K. Kaul, On impulsive semidynamical systems, J. Math. Anal. Appl. 150 (1990), 120–128.
S.K. Kaul, Stability and asymptotic stability in impulsive semidynamical systems, J. Applied Math. Stochastic Anal. 7(4) (1994), 509–523.
J. Vasundhara Devi and N. Giribabu, On hybrid Caputo fractional differential equations with variable moments of impulse, Eur. J. Pure Appl. Math. 7 (2014), 115–128.
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