###### Abstract
The analytic solution to the Localized LQR (LLQR) optimum control challenge was developed in [36]. Paper [37] showed how an infeasible primal-dual interior point technique can be utilized to efficiently solve a robust optimum control problem with possible uses to model predictive control. The tasks of multicriteria optimization in controlling technological systems are reduced to multicriteria problems of fuzzy mathematical programming, and a heuristic algorithm for solving the formulated problem of optimal control is developed based on modifying the principles of maximin and Pareto optimality, [38]. In [39], a formulation of the problem of multicriteria optimization is obtained, considering the partial fuzziness of the starting information. A heuristic method for its solution is proposed, which is based on the experience of the decision maker. [PERSON] in [40] was one of the first to study the transient response of linear systems with nonzero initial conditions. After that, study in this area diminished; thus, transient response referred to the system's reaction under zero initial conditions and with a unit step function of the input. In [41], [PERSON] proved that if the closed system's poles are displaced far to the left in the complex plane, substantial deviations of the trajectory from the coordinate origin are unavoidable. In [42], [PERSON] et al. continue the work of [PERSON] and [PERSON] on transient response in systems with nonzero initial conditions. This was accomplished by proposing a more precise estimate of the overshoot amplitude and demonstrating that large deviations produce effects for different pole locations. They also looked at determining the upper deviation limit using the linear matrix inequalities approach (LMI). The theoretical basis for this research is, first of all, the concept of the full transfer function matrix defined for linear discrete systems, and then the TS type of fuzzy systems, with application in modeling, identification and control of dynamical systems. A full transfer function matrix, which was introduced and developed in [43; 44; 45], resolved controversy between the system transfer function and the stability testing using a classical transfer function. It is well understood that system stability, by definition, represents a dynamical attribute of the system in the free working regime for all zero input and variable arbitrary unknown initial conditions. The transfer function is defined for the system in the forced working regime under nonzero input and all zero initial conditions. This concept was applied in articles [1; 2]. In these papers, the area of relative stability was derived, where the closed system has a predetermined damping coefficient. After that, conditional optimization was performed in the cases of proportional-difference-sum-type linear controllers with two and three adjustable parameters. A new performance index is presented that is entirely compatible with the use of the full transfer function matrix. The output error used in the performance index is influenced by all actions at the same time: by external inputs and by nonzero initial conditions. Based on the conclusion that the optimal parameters obtained for zero are not optimal for nonzero initial conditions, in the case of linear discrete systems, it is intuitively imposed that something similar can also be valid in the case of nonlinear discrete systems. In order to apply the full transfer function (which, of course, applies to linear systems), the property that TS fuzzy systems can represent a class of nonlinear dynamical systems, composed of linear (or linearized) subsystems, is used. In this way, it is possible to use the full transfer function matrix, define new control algorithms, and determine the optimal parameters of the controller in the case of nonzero initial conditions. Compared with existing approaches, a new conditional optimization procedure based on the full transfer matrix is used in this paper.