Generalized exponential functions for system analysis and synthesis. (English) Zbl 0283.93002
Summary: Generalized exponential functions are defined and developed for the analysis and synthesis of dynamical systems. Approximation of conventional response transforms in the \(s\)-domain is implemented by utilizing non-integer-order complex operator \(s^v\). The analysis technique is applied to a non-inductive long cable and to network systems. In addition, for the synthesis, Laguerre-Lee functions in the \(s\)-domain are extended into the non-integer-order \(s^v\)-domain in terms of generalized exponential functions. The application is demonstrated by an example.
MSC:
| 93A10 | General systems |
| 93Cxx | Model systems in control theory |
| 94C11 | Switching theory, applications of Boolean algebras to circuits and networks |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 33E99 | Other special functions |
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