Admissible measurement noise of variance-constrained satisfactory filter

An error-variance constrained satisfactory filter is studied for a class of linear discrete-time stochastic systems with given model noise such that the designed filter admits the system to have time invariant measurement noise with intensity as large as possible. Finally, an LMI-based solution to steady current-estimation-type Kalman filter is presented via the minimal variance characteristic of Kalman filter when both intensities of the model noise and measurement noise are fixed. Then the problem to find the constrained satisfactory filter is transformed via LMI approach to a minimum one subjected to a LMI constraint. The latter can be effectively solved by means of Matlab-LMI software. Finally an example is proposed to demonstrate the obtained results