Suboptimal robust filtering of states of finite dimensional linear systems with time-varying parameters under nonrandom disturbances

This paper deals with the construction and analysis of the properties of a robust filter that can perform the estimation, guaranteeing the necessary accuracy, of the states of a linear time-varying uncertain multidimensional system, subject to nonrandom disturbances. The time varying parameters of the system are supposed to be uncertain belonging to some given bounded class of system parameters. The external disturbances are supposed to be of limited power less than some prespecified value. The suggested robust filter has a Kalman´s structure with a gain matrix which is a definite positive solution of a matrix Ricatti equation. In order to achieve a better precision in the filtration process, a minimization process employing the frequency condition is suggested