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On the solvability of DC equations and the implicit integration formula

1973; Wiley; Volume: 1; Issue: 3 Linguagem: Inglês

10.1002/cta.4490010307

1097-007X

Tamás Roska, J. Klimó,

Control and Stability of Dynamical Systems

Abstract The paper contains the following new results concerning the solvability of the DC equations and the implicit integration formula of a broad class of nonlinear networks. A new method of proof is given. Conditions are given for checking the unique solvability of the DC equation F(x)+Ax = b in case of monotone (not strictly monotone) and ‘steep’ characteristics and in the case when the characteristics have negative slope. Furthermore existence theorems are given under very weak conditions. In the case of a broad class of nonlinear networks sufficient conditions are presented for the unique solvability of the implicit integration formula when the characteristics are monotone or have negative slope. Some practical consequences of the theorems are also discussed.