Time-invariant approach to set-membership simulation and state observation for discrete linear time-invariant systems with parametric uncertainty

In this paper, a new algorithm for set-membership simulation and state observation of discrete linear time-invariant systems with structured uncertainty is proposed. It solves the problem of set-membership simulation and state observation determining, through optimisation, the minimum volume outer box (interval) enclosing the system states at every iteration. The originality of the algorithm is that considers the case of parametric time-invariant uncertainties. Several previous algorithms have considered the case of parametric time-varying uncertainties. However, recently it has been presented possible unstability problems when simulating a time-invariant uncertain system as it were time varying, being this result the motivation for the approach proposed in this paper. Finally, an example of application of the proposed approach for set-membership simulation and observation is presented.