Oscillation for a class of delay direct control systems. (English) Zbl 0657.93033
The paper studies linear delay equations perturbed by a nonlinear feedback and gives sufficient conditions for oscillations and for nonoscillations, i.e., for the property that the norm of solutions has arbitrarily large zeros. The proofs use differential inequalities.
Reviewer: F.Colonius
MSC:
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
| 34K35 | Control problems for functional-differential equations |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 93C05 | Linear systems in control theory |
Keywords:
linear delay equations; nonlinear feedback; oscillations; nonoscillations; differential inequalitiesReferences:
| [1] | Ladee, G. S.; Zhang, B. G., Oscillation and nonoscillation for system of two first-order linear differential equations with delay, J. Math. Anal. Appl., 115, 57-75 (1986) · Zbl 0607.34060 |
| [2] | Kartsatos, A. G.; Walters, T., Some oscillation results for matrix and vector differential equations with Forcing term, J. Math. Anal. Appl., 73, 506-513 (1980) · Zbl 0447.34034 |
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