Observability of Discrete-Time LTI Systems Under Unknown Piece-Wise Constant Inputs

Vipul Kumar Sharma, Pavankumar Tallapragada

Abstract: This letter is on observability of discrete-time LTI systems under unknown piece-wise constant inputs with sufficiently slow, but arbitrary update times. Assuming knowledge of the update times, we characterize the unobservable subspace and show that with sufficiently many measurements in each inter-update interval of the input, the unobservable subspace remains fixed. We explore the implications of the result for privacy in event-triggered control through an illustrative example.