Observability of linear differential-algebraic equations in the class of Chebyshev functions. (Russian. English summary) Zbl 1373.34098
From the summary: We consider linear time-varying systems of first order ordinary differential equations unresolved with respect to the derivative of the unknown function and identically degenerate in the domain. The unsolvability measure with respect to the derivatives for some DAE is an integer that is called the index of the DAE. We admit an arbitrarily high unsolvability index not more than the order of the system. The analysis is carried out under the assumption of a structural form with separated differential and algebraic subsystems.
We investigate the observability of a DAE by a given scalar output. We obtain a sufficient condition of \(R\)-observability (observability in the reachable set) of linear non-stationary systems of DAE in the class of Chebyshev polynomials. We consider the example illustrating the obtained results.
We investigate the observability of a DAE by a given scalar output. We obtain a sufficient condition of \(R\)-observability (observability in the reachable set) of linear non-stationary systems of DAE in the class of Chebyshev polynomials. We consider the example illustrating the obtained results.
MSC:
| 34H05 | Control problems involving ordinary differential equations |
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
| 93B07 | Observability |
| 34A30 | Linear ordinary differential equations and systems |
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