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**Analysis of impulsive modes and Luenberger observers for descriptor systems.**
*(English)*
Zbl 0986.93010

Summary: The distinction between impulsive modes that can be generated by inputs and impulsive modes that can only be generated by initial conditions is investigated for linear time-invariant descriptor systems. It reveals that the input-generable impulsive modes are very crucial for the existence of normal Luenberger observers of the systems. Based on this observation, an earlier known concept called strong detectability for regular descriptor systems is extended to the irregular case, which is shown to be of much clearer physical meaning in a classical sense than a recently proposed equivalent notion of causal detectability. Thus, similar to the regular case, strong detectability is also a sufficient and necessary condition for the existence of normal Luenberger observers for irregular descriptor systems.

### MSC:

93B07 | Observability |

34A09 | Implicit ordinary differential equations, differential-algebraic equations |

### Keywords:

descriptor systems; singular systems; observability; detectability; Luenberger observers; impulsive modes
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\textit{W. Wang} and \textit{Y. Zou}, Syst. Control Lett. 44, No. 5, 347--353 (2001; Zbl 0986.93010)

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### References:

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