Refinement Methods for State Estimation via Sylvester-Observer Equation

Table 1

Implementation of block refinement method to solve the Sylvester equation with different values of 𝑚.

𝑚	𝑟	ℓ	‖𝑉^𝑇𝑚𝐴^𝑇𝑉𝑚−𝐴𝑚‖	‖𝑊^𝑇𝑚𝐹𝑊𝑚−𝐹𝑚‖	Iteration	Time
10	2	5	4.11𝐸−014	3.71𝐸−016	482	12.03
20	2	10	6.32𝐸−014	5.97𝐸−015	391	10.08
30	2	15	1.16𝐸−013	7.34𝐸−015	319	8.26
40	2	20	3.65𝐸−013	8.89𝐸−014	225	6.03
50	2	25	2.01𝐸−012	9.39𝐸−014	171	4.47
60	2	30	4.73𝐸−012	1.44𝐸−013	67	2.46