Some remarks on local activity and local passivity. (English) Zbl 1366.93244
Summary: We study local activity and its contrary, local passivity, for linear systems and show that generically an eigenvalue of the system matrix with positive real part implies local activity. If all state variables are port variables we prove that the system is locally active if and only if the system matrix is not dissipative. Local activity was suggested by Leon Chua as an indicator for the emergence of complexity of nonlinear systems. We propose an abstract scheme which indicates how local activity could be applied to nonlinear systems and list open questions about possible consequences for complexity.
MSC:
| 93C05 | Linear systems in control theory |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 93C10 | Nonlinear systems in control theory |
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