###### Abstract  
The study proposes a novel method for synthesis of a discrete-time parallel distributed compensation (PDC) controller for the nonlinear discrete-time Takagi-Sugeno (TS) fuzzy plant model. For each of the fuzzy plant model linear subsystems, a local linear first order proportional-sum (PS) controller is designed. The algebraic technique is used in two-dimensional parameter space, utilizing the characteristic polynomial of the row nondegenerate full transfer function matrix. Each system's relative stability is accomplished in relation to the selected damping coefficient. The supplementary criterion is the minimal value of the performance index in the form of the sum of squared errors (SSE). However, unlike the traditional technique, output error is influenced by all simultaneous actions on the system: nonzero inputs and nonzero initial conditions. The full transfer function matrix of the system allows for the treatment of  
of the situation is given in [3]. Just some of the examples are [4; 5]. The solution of designing a discrete controller for a discrete plant is discussed in [4]. Paper [5] proposes a control parametrization-based optimum PID tuning technique for a single-link manipulator. The control system's performance specifications are expressed as continuous state inequality constraints. The single-link manipulator's PID optimum tuning issue may thus be framed as an optimal parameter selection problem with continuous inequality constraints. The constraint transcription approach, in conjunction with a local smoothing technique, handles these continuous inequality requirements. As a result, ref. [6] presents an optimum design strategy for the PID parameters in discrete-time systems for maximizing the reference tracking and disturbance rejection performances, respectively. For every given linear time-invariant (LTI) plant, ref. [7] tackles the challenge of defining the set of all stable PID type controllers without parametric models. The frequency response data and the number of right-half-plane (RHP) poles of the plant are shown to be the only information needed for designing, and all stabilizing domains in the parameter space of PID-type controllers are determined by the boundaries, which are analytically described using the D-decomposition technique. Other research studies found a stability region in the parameter space as well. Authors accomplished it in the state space form for both discrete-time systems and also for continuous time in [8]. In the root signs invariant regions, researchers decomposed the area in the parameter plane for a continuous-time system in the state space form [9]. [PERSON] and [PERSON] [10] dealt with a trinomial discrete equation with two delays and offered a criterion for evaluating Lyapunov stability reliant on parameter values, as well as an extension of the Lyapunov stability theory via the new \(r-\)stability concept. [PERSON] et al. [11] outlined the state of the art for continuous-time system parameter synthesis beginning with [PERSON] and went over [PERSON] to the present, with latest additions and unique results that relate to the stability domain in the parameter space and considering the \(H_{\infty}\) criterion, robustness, uncertainty and so on. Plant control using the traditional control algorithm has been very relevant from the past to the present day, and researchers are actively experimenting with it. The DC servo motor is often the object of automatic control and has a very wide range of applications, which can be seen on the basis of the following works. Article [12] introduced deterministic artificial intelligence (D.A.I.) to control direct current motors used by unmanned underwater vehicles. Paper [13] describes how to regulate the speed of a permanent magnet direct current motor using a buck converter with Zero Average Dynamics.