Abstract
We investigate a scalar characteristic exponential polynomial with complex coefficients associated with a first order scalar differential-difference equation. Our analysis provides necessary and sufficient conditions for allocation of the roots in the complex open left half-plane what guarantees asymptotic stability of the differential-difference equation. The conditions are expressed explicitly in terms of complex coefficients of the characteristic exponential polynomial, what makes them easy to use in applications. We show examples including those for retarded PDEs in an abstract formulation.
| Original language | English |
|---|---|
| Pages (from-to) | 607-629 |
| Number of pages | 23 |
| Journal | Archives of Control Sciences |
| Volume | 33 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2023 |
Keywords
- characteristic exponential polynomial of differential-difference equation
- first order differential-difference equation with complex coefficients
- retarded differential-difference equation (DDE)
- stability of differential-difference equation
ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization
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