Finite escapes and convergence properties of guaranteed-cost robust filters

Abstract

The design of robust filters for linear time-varying systems subject to parameter perturbations is considered. The design is based on the minimization of an upper bound for the error covariance. The computation of the filter matrices calls for the solution of a pair of differential Riccati equations parameterized by a scalar design parameter. The main results of the paper concern the asymptotic properties of the filter when it is applied to time-invariant systems. Differently from the standard Kalman filter, the robust filter may abruptedly cease to exist owing to the presence of finite escape times in the associated Riccati equations. Nevertheless, provided that the parameter perturbations do not affect the unstable dynamics, convergence to a stable steady-state filter can always be ensured by properly adjusting the scalar design parameter. Since such an adjustment might deteriorate the steady-state performance, a time-varying strategy for the tuning of the scalar parameter is developed in order to guarantee both convergence and performance.