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On the Modulating Function Method for Discrete-Time Systems: Any Sequence Suffices
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DOI：10.1109/tac.2026.3719442.png)
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Abstract
En 中文
The modulating function method has been studied for parameter and state estimation of many system classes, such as linear, nonlinear, fractional-order, and distributed systems. However, only continuous-time systems have been considered so far, despite the fact that the implementation for simulations or practical applications is typically done in discrete time. Furthermore, mathematical models found in economics and biology are directly described by recurrence relations. To fill this research gap, discrete-time modulating functions are investigated and proposed, effectively extending the domain of use of the modulating function method. In doing so, a rather surprising result is obtained: any bounded sequence of numbers can be trivially converted into a discrete modulating function. Moreover, parameter and difference estimation algorithms for linear systems are proposed and discussed, along with their robustness to additive disturbances, as well as modulation-based state estimators for LTI, LTV, and a class of nonlinear systems. Lastly, the connection between the modulating function method and observer structures, including the Kalman filter, is shown to also exist in discrete time.
Keywords:
Auxiliary systems
discrete-time
estimation
modulating function method
observers
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W
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