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. Min-max, optimality, sliding-mode control. . He conducts research in sliding-mode control with applications to reusable launch vehicle control, aircraft reconfigurable flight control systems, missile control systems, an autonomous conventional, and nuclear reactor systems of electric power supply. He published over 120 technical papers. Carlos Jiménez Gallegos was born in 1975 at San Luis Potosí, México. He received the Bc.Sc. degree in electronic engineering and the Ms.Sc. degree from the University of San Luis Potosí, México, in 1999 and 2000, respectively. He is currently working toward the D.Sci. degree in robust and min-max multimodal optimization at the same university. His research interests include robust control of nonlinear dynamical systems, optimal control, and game theory. Index Terms-

A two person prey-predator (cvader-pursuit) dynamic linear quadratic game'is considered. In gcncral, this problem belong to thc class of non-zero sum dynamic games. An original dynamic lincar timc varying system with additive disturbances or uncertainties is rcplaced by a finite set of dynamic models such that cach one describes a particular uncertain caSe including cxact realizations of possihlc dynamic equations as well as external bounded disturbances. Each model from a givcn finite set is characterizcd by a quadratic performma index. The devcloped minimax LQ control strategy provides a Nash equilibrium in the given mini-max diffcrential game. This problem is shown t o be reduced to finding of a Nash equilibrium point in a finite dimensional simplex.

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