\(h\)-stability for linear dynamic equations on time scales

DOI10.1016/j.jmaa.2005.12.046zbMath1112.34031OpenAlexW1981311117MaRDI QIDQ855675

Sung Kyu Choi, Dong Man Im, Nam Jip Koo

Publication date: 7 December 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.12.046

zbMATH Keywords

\(h\)-stabilityquadratic Lyapunov functionlinear dynamic equation

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Perturbations of ordinary differential equations (34D10) Difference equations, scaling ((q)-differences) (39A13) Asymptotic properties of solutions to ordinary differential equations (34D05) Partial difference equations (39A14)

Related Items (19)

Variationally stable dynamic systems on time scales ⋮ \(h\)-stability in \(p\)th moment of neutral pantograph stochastic differential equations with Markovian switching driven by Lévy noise ⋮ \(h\)-stability for nonlinear abstract dynamic equations on time scales and applications ⋮ \(\psi\)-exponential stability of nonlinear impulsive dynamic equations on time scales ⋮ On the exponential stability of dynamic equations on time scales ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A converse theorem on practical \(h\)-stability of nonlinear systems ⋮ \(h\)-stability for stochastic Volterra-Levin equations ⋮ Asymptotic stability for nonlinear time-varying systems on time scales ⋮ Stability of abstract dynamic equations on time scales by Lyapunov's second method ⋮ Stability of linear dynamic systems on time scales ⋮ \(h\)-stability of dynamic equations on time scales with nonregressivity ⋮ On uniform \(h\)-stability of non-autonomous evolution equations in Banach spaces ⋮ Unnamed Item ⋮ An LMI approach to stability for linear time-varying system with nonlinear perturbation on time scales ⋮ On the stability of linear dynamic systems on time scales ⋮ Sufficient conditions for uniform exponential stability and \(h\)-stability of some classes of dynamic equations on arbitrary time scales ⋮ Time scale state feedback h-stabilisation of linear systems under Lipschitz-type disturbances

Cites Work

• Analysis on measure chains - a unified approach to continuous and discrete calculus
• Integral inequalities of Gronwall-Bellman-Bihari type and asymptotic behavior of certain second order nonlinear differential equations
• Perturbations of nonlinear systems of difference equations
• Variationally stable difference systems by \(n_\infty\)-similarity
• Dynamic equations on time scales: A survey
• Stability for time varying linear dynamic systems on time scales
• Inequalities on Time Scales: A Survey
• PERTURBATIONS OF ASYMPTOTICALLY STABLE DIFFERENTIAL SYSTEMS
• Stability of nonlinear differential systems^*
• Variationally stable difference systems
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