Abstract: Here we consider time-dependent linear systems of the formwith state ∈ , control (input) ∈ , and output ∈ . The main results of this paper are local characterizations of observability and strong observability (or observability with unknown inputs) of (, ) and (, , ). These criteria are pointwise rank conditions on a certain matrix, which is explicitly built up from the first − 2 derivatives of and and the first − 1 derivatives of . The results generalize well-known theorems for time-invariant systems. The proofs lead also to observers (with and without the input), and the main tool is a generalized product rule for the differentiation of a product of matrices, where only one factor and the product itself are known to be differentiable.
Publication Year: 2001
Publication Date: 2001-06-01
Language: en
Type: article
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