Distributed State Observer for Systems with Multiple Sensors under Time-Delay Information Exchange

. 2024 Jul 5;24(13):4382. doi: 10.3390/s24134382

Algorithm 1 Algorithm for constructing a distributed observer

1:
Solve LMI (16) to obtain $P_{o} > 0$ , $P_{u} > 0$ , $Q_{o} > 0$ , $Q_{u} > 0$ and $X_{d}$ ;
2:
Calculate $K_{d} = P_{o}^{- 1} X_{d}$ , and then obtain $K_{i d} = K_{d} (({\bar{v}}_{i - 1} + 1) : {\bar{v}}_{i}, ({\bar{p}}_{i - 1} + 1) : {\bar{p}}_{i})$ , ( $i = 1, \dots, N$ );
3:
Calculate $K_{i} = T_{i}^{T} [\begin{matrix} K_{i d} \\ 0_{(n - v_{i}) \times p_{i}} \end{matrix}]$ , ( $i \in N$ );
4:
Construct distributed observer (3) to obtain ${\hat{x}}_{i}$ .