Multimodel and ISM control

Here, an original linear time-varying system with matched and unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations also as external unmatched bounded disturbances. Such a trade-off between an original uncertain linear time-varying dynamic system and a corresponding higher-order multimodel system containing only matched uncertainties leads to a linear multimodel system with known unmatched bounded disturbances and unknown matched disturbances as well. Each model from a given finite set is characterized by a quadratic performance index. The developed min–max integral sliding mode control strategy gives an optimal min–max linear quadratic (LQ) control with additional integral sliding mode term. The design of this controller is reduced to a solution of an equivalent min–max LQ problem that corresponds to the weighted performance indices with weights from a finite-dimensional simplex. The additional integral sliding mode controller part completely dismisses the influence of matched uncertainties from the initial time instant. Two numerical examples illustrate this study.