DocumentCode :
1171031
Title :
Stability and instability criteria for nonlinear distributed networks
Author :
Willson, Alan N., Jr.
Volume :
19
Issue :
6
fYear :
1972
fDate :
11/1/1972 12:00:00 AM
Firstpage :
615
Lastpage :
622
Abstract :
Electrical networks consisting of lumped linear and memoryless nonlinear elements and an arbitrary number of lossless transmission lines are considered. It is shown that a large class of such networks can be described by a system of functional-differential equations having the form \\dot{x}(t) =f(x_{t}) , where the state of the system at time t \\geq 0 is represented by x_{t} , a point in the space C_{H}((- \\infty ,0], E^{n}) of bounded continuous functions mapping the interval (-\\infty , 0] into E^{n} , with the compact open topology, and the function f mapping C_{H}(( - \\infty , 0], E^{n}) into E^{n} is continuous and Lipschitzian. A Lyapunov functional is presented and used to obtain several theorems concerning the stability and instability of the equilibrium solution of such networks.
Keywords :
Distributed-lumped networks; Lyapunov methods; Nonlinear distributed networks; Nonlinear networks; Stability; Convergence; Differential equations; Extraterrestrial measurements; Network topology; Nonlinear equations; Propagation losses; Stability criteria; Telephony; Transmission line theory;
fLanguage :
English
Journal_Title :
Circuit Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9324
Type :
jour
DOI :
10.1109/TCT.1972.1083546
Filename :
1083546
Link To Document :
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