Observability of linear time-invariant descriptor systems with a derivative in the output

The observability, including complete observability, ℛ -observability and impulse observability, problems of linear time-invariant descriptor systems with a derivative in the output are studied. Necessary and sufficient conditions are given about complete observability, ℛ-observability and impulse observability. From which, several simple sufficient conditions for the complete observability are presented. Furthermore, differences of the complete observability are explained between the systems with a derivative and those without a derivative in the output.

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