TY - JOUR
T1 - Stability of partial functional integro-differential equations
AU - Agarwal, R. P.
AU - Domoshnitsky, A.
AU - Goltser, Ya
N1 - Funding Information:
2000 Mathematics Subject Classification. 34K15, 35B05. Key words and phrases. Functional differential equations, exponential stability, Cauchy matrix, phase transition model. This research was supported by the program KAMEA of the Ministry of Absorption of the State of Israel.
PY - 2006/1
Y1 - 2006/1
N2 - Using the Fourier method of separation of variables and a procedure proposed in this paper, namely, reducing integrodifferential equations to systems of ordinary differential equations, the exponential stability of partial functional integro-differential equations is studied. Various tests for the exponential stability are proposed. In contrast to many other known methods our approach does not assume the smallness of integral terms. This allows us to use the method for stabilization of processes described by unstable differential equations by adding controls in the form of integral terms. Finally, using our approach, a phase transition model is analyzed.
AB - Using the Fourier method of separation of variables and a procedure proposed in this paper, namely, reducing integrodifferential equations to systems of ordinary differential equations, the exponential stability of partial functional integro-differential equations is studied. Various tests for the exponential stability are proposed. In contrast to many other known methods our approach does not assume the smallness of integral terms. This allows us to use the method for stabilization of processes described by unstable differential equations by adding controls in the form of integral terms. Finally, using our approach, a phase transition model is analyzed.
KW - Cauchy matrix
KW - Exponential stability
KW - Functional differential equations
KW - Phase transition model
UR - http://www.scopus.com/inward/record.url?scp=33645831382&partnerID=8YFLogxK
U2 - 10.1007/s10450-006-9681-x
DO - 10.1007/s10450-006-9681-x
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AN - SCOPUS:33645831382
SN - 1079-2724
VL - 12
SP - 1
EP - 31
JO - Journal of Dynamical and Control Systems
JF - Journal of Dynamical and Control Systems
IS - 1
ER -