Continuous Time-varying System
Consider the continuous linear time-variant system
Suppose that the matrices are given as well as inputs and outputs for all then it is possible to determine to within an additive constant vector which lies in the null space of defined by
where is the state-transition matrix.
It is possible to determine a unique if is nonsingular. In fact, it is not possible to distinguish the initial state for from that of if is in the null space of .
Note that the matrix defined as above has the following properties:
- is symmetric
- is positive semidefinite for
- satisfies the linear matrix differential equation
- satisfies the equation
Read more about this topic: Observability
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