Strong Observability of Time-Dependent Linear Systems

Abstract

There are considered time-dependent linear systems of the form with state x ∈ IR ⁿ, control (input) u ∈ IR ^m and output y ∈ IR ^p. We derive local characterizations of observability of (A, C) and strong observability of (A, B, C). These criteria are pointwise rank conditions on a certain matrix, which is explicitly built up from the first n — 2 derivatives of A and B and the first n — 1 derivatives of C. The results generalize well-known theorems for time-invariant systems.