Minimum Structural Sensor Placement for Switched Linear Time-Invariant Systems and Unknown Inputs

Abstract: In this paper, we study the structural state and input observability of continuous-time switched linear time-invariant systems and unknown inputs. First, we provide necessary and sufficient conditions for their structural state and input observability that can be efficiently verified in $O((m(n+p))^2)$, where $n$ is the number of state variables, $p$ is the number of unknown inputs, and $m$ is the number of modes. Moreover, we address the minimum sensor placement problem for these systems by adopting a feed-forward analysis and by providing an algorithm with a computational complexity of $ O((m(n+p)+\alpha)^{2.373})$, where $\alpha$ is the number of target strongly connected components of the system's digraph representation. Lastly, we explore different assumptions on both the system and unknown inputs (latent space) dynamics that add more structure to the problem, and thereby, enable us to render algorithms with lower computational complexity, which are suitable for implementation in large-scale systems.