Min-max sliding-mode control for multimodel linear time varying systems

An original linear time-varying system with 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 as well as external bounded disturbances. Such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system with a complete knowledge leads to a linear multi-model system with known bounded disturbances. Each model from a given finite set is characterized by a quadratic performance index. The developed min-max sliding-mode control strategy gives an optimal robust sliding-surface design algorithm, which is reduced to a solution of an equivalent linear quadratic problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex. An illustrative numerical example is presented.