About robust stability of dynamic systems with time delays through fixed point theory

DOI10.1155/2008/480187zbMath1181.47079OpenAlexW2144396717WikidataQ57675372 ScholiaQ57675372MaRDI QIDQ1008522

Manuel de la Sen

Publication date: 30 March 2009

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/45414

zbMATH Keywords

fixed pointasymptotic stabilitydelay differential equationlinear differential equationfeedback control system

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Stability theory of functional-differential equations (34K20) Linear functional-differential equations (34K06) Control problems for functional-differential equations (34K35) Applications of operator theory in systems, signals, circuits, and control theory (47N70)

Related Items

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets ⋮ About periodicity of impulsive evolution equations through fixed point theory ⋮ Fixed point and best proximity theorems under two classes of integral-type contractive conditions in uniform metric spaces ⋮ On \(p\)-cyclic orbital M-K contractions in a partial metric space ⋮ Fixed and best proximity points of cyclic jointly accretive and contractive self-mappings ⋮ Stable iteration procedures in metric spaces which generalize a Picard-type iteration ⋮ Some properties of distances and best proximity points of cyclic proximal contractions in metric spaces ⋮ Asymptotically non-expansive self-maps and global stability with ultimate boundedness of dynamic systems ⋮ On the extensions of Krasnoselskii-type theorems to \(p\)-cyclic self-mappings in Banach spaces ⋮ Some fixed point properties of self-maps constructed by switched sets of primary self-maps on normed linear spaces ⋮ Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings ⋮ Fixed points and exponential stability for impulsive time-delays BAM neural networks via LMI approach and contraction mapping principle ⋮ On bounded strictly positive operators of closed range and some applications to asymptotic hyperstability of dynamic systems ⋮ Stability and convergence results based on fixed point theory for a generalized viscosity iterative scheme ⋮ Some combined relations between contractive mappings, Kannan mappings, reasonable expansive mappings, and \(T\)-stability ⋮ Total stability properties based on fixed point theory for a class of hybrid dynamic systems ⋮ Novel criteria on global robust exponential stability to a class of reaction-diffusion neural networks with delays ⋮ On best proximity results for a generalized modified Ishikawa's iterative scheme driven by perturbed 2-cyclic like-contractive self-maps in uniformly convex Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Perron type theorem for functional differential equations
• Global attractivity in an almost periodic multi-species nonlinear ecological model
• Estimation of parameters in carbon sequestration models from net ecosystem exchange data
• Time lags can control algal bloom in two harmful phytoplankton-zooplankton system
• Convergence theorems of fixed points for a finite family of nonexpansive mappings in Banach spaces
• Fixed point methods for the generalized stability of functional equations in a single variable
• Fixed points and stability in neutral stochastic differential equations with variable delays
• A fixed point approach to the stability of a functional equation of the spiral of Theodorus
• Controllability of nonlinear integro-differential third order dispersion system
• Exact controllability of nonlinear diffusion equations arising in reactor dynamics
• Stability and periodic solutions of ordinary and functional differential equations
• Linear integro-differential equations in Banach spaces
• Introduction to functional differential equations
• Delay effects on stability. A robust control approach
• Positive solutions and asymptotic behavior of delay differential equations with nonlinear impulses
• On the uniform exponential stability of a wide class of linear time-delay systems.
• An algebraic method for pole placement in multivariable systems with internal and external point delays by using single rate or multirate sampling
• The stabilizability of integro-differential systems with two distributed delays
• Profitless delays for a nonautonomous Lotka-Volterra predator-prey almost periodic system with dispersion
• On positivity of singular regular linear time-delay time-invariant systems subject to multiple internal and external incommensurate point delays
• A note on asymptotic contractions
• On impulsive time-varying systems with unbounded time-varying point delays: Stability and compactness of the relevant operators mapping the input space into the state and output spaces
• Stability of impulsive time-varying systems and compactness of the operators mapping the input space into the state and output spaces
• Asymptotic stability of nonlinear functional differential equations
• Stability of Solutions of Linear Delay Differential Equations
• Discretization and FIR filtering of continuous linear systems with internal and external point delays

This page was built for publication: About robust stability of dynamic systems with time delays through fixed point theory