Construction of Lyapunov Functionals for Networks of Coupled Delay Differential and Continuous-Time Difference Equations
نویسندگان
چکیده
To address various types of delays including the neutral-type arising in dynamical networks, this paper deals with coupled delay differential and continuous-time difference equations and develops stability and robustness criteria. Subsystems described by differential equations are not required to be input-to-state stable. No assumptions on network topology are made. To tackle networks in such a general formulation, this paper explicitly constructs Lyapunov-type functionals establishing stability and robustness of the overall networks. The construction requires only simple characterizations of subsystems in terms of inequalities with Lyapunov functions and instantaneous norms.
منابع مشابه
Method of Lyapunov functionals construction in stability of delay evolution equations
The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The general method of Lyapunov functionals construction which was proposed by V. Kolmanovskii and L. Shaikhet and successfully used already for functional differential equations, for difference equations with discrete time, for difference equations with continuous time, is used he...
متن کاملLyapunov Functionals Construction for Stochastic Difference Second-kind Volterra Equations with Continuous Time
The general method of Lyapunov functionals construction which was developed during the last decade for stability investigation of stochastic differential equations with aftereffect and stochastic difference equations is considered. It is shown that after some modification of the basic Lyapunov-type theorem, this method can be successfully used also for stochastic difference Volterra equations w...
متن کاملConstruction of Lyapunov functionals for stochastic difference equations with continuous time
One general method of Lyapunov functionals construction which was used earlier both for stochastic differential equations with aftereffect and for stochastic difference equations with discrete time here is applied for stochastic difference equations with continuous time. © 2004 IMACS. Published by Elsevier B.V. All rights reserved.
متن کاملGeneral Method of Lyapunov Functionals Construction in Stability Investigations of Nonlinear Stochastic Difference Equations with Continuous Time
The general method of Lyapunov functionals construction has been developed during the last decade for stability investigations of stochastic differential equations with aftereffect and stochastic difference equations. After some modification of the basic Lyapunov type theorem this method was successfully used also for difference Volterra equations with continuous time. The latter often appear a...
متن کاملStability in Functional Difference Equations Using Fixed Point Theory
When dealing with nonlinear functional differential or difference equations, it is popular to use the concept of Lyapunov functionals to qualitatively analyze their behavior. However, the use of Lyapunov functionals require ingenuity in the construction of such a function and moreover, the end results heavily depend on the constructed Lyapunov functional. For the purpose of illustration we cons...
متن کامل