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The proposed observer structure takes advantage of the general observability characterization presented in Vázquez et al.
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Unlike the general controllability and observability problems which require each state to be controllable and observable, we only examine the consensus state to be controllable and the tracking error states between the followers and the leader to be observable.
However, the general principles of observability and controllability can be applied both locally and globally.
In general, neither controllability nor observability or any specific system representation is required.
The approach proposed here may be used for a process based on a continuous model in the time domain, with two assumptions on the observability and the general structure of the model.
Basic observability notions and observer structures are first recalled, together with ingredients for advanced designs on this basis.
Comparisons are made under different observation scenarios (full observability and different types of partial observability).
Observability analysis of the relative state is done and the general mathematical expression of the observable condition is obtained.
In this section, we introduce a general Lyapunov operator and the notion of exact observability of stochastic time-delay deference systems.
Others, for example the connection between symmetry breaking and observability, are particular aspects of the general issue concerning the status and significance of physical symmetries, but in the case of SSB they take on a stronger force: what is the epistemological status of a theory based on "hidden" symmetries and SSB?
The traditional passive-type state reconstruction that does not require input design will fail in general, even if the system has a full-rank observability matrix.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com