The linear-quadratic problem in the system with proportional controllers is considered. New necessary conditions for establishing optimal values of gains Ki are determined which are very simple and convenient for calculations. New properties of the Hurwitz matrix are also discovered. The proposed method is alternative to the well known algebraic Riccati equations.

Invariant recognition of 2D binary image often arises from image moments. They enable the construction of affine transform, which ensures the invariance to translation, scaling, first rotation and stretching of the image. It is a problem to ensure the invariance to the second rotation. The paper deals with two methods how to realize the affine invariant recognition system with the numerical stable elimination of the second rotation. Modified images are obtained via polar or Radon's transform. Mentioned two approaches enable affine invariant systems construction and they were used for analysis of particles in granular mixtures. The affine invariant system is applied to detail analysis of fertilizer grains.

Combinations and Genetic Algorithms for the Locations and tuning of Robust Power System Stabilizers (PSS's) is presented in this paper. The PSS parameters and locations are computed to assure maximum damping performance under different operating conditions. The efficacy of this technique in damping local and inter-area modes of oscillations in multimachine power systems is confirmed through nonlinear simulation results and eigenvalues analysis.

This paper describes application of linear and nonlinear Model Predictive Control (MPC) algorithms to a cyclohexane-heptane distillation column. Two nonlinear MPC techniques are compared in terms of control accuracy and computational complexity: MPC with Nonlinear Optimization (MPC-NO) and MPC with Nonlinear Prediction and Linearization (MPC-NPL). In nonlinear MPC a feedforward neural model is used rather than significantly complicated and causing numerical problems fundamental model of the process.

In the paper a problem of the on-line model identification of secondary and feedback paths in the feedforward ANC system is considered. The system is closed-loop, with low signal-to-noise ratio and with the disturbance affecting the input and output of the identified paths. To overcome the mentioned difficulties a new approach to the identification based on the higher-order spectra is presented. The integrated bispectrum-based identification method is proposed and the results of its applying are provided and compared with the results derived from the classical methods. The estimates are computed on the basis of data acquired in the laboratory (real-world) experiment as well as in the computer simulations.

In this paper, a new approach of linguistic fuzzy modeling proposed by Ben-Ghalia et al. is applied to induction motor. Thus, a classical model is first given together with the most used asynchronous motor control strategy, which is the pole assignment. After more, in order to minimize the dependence of the system to parameter variations and external perturbations, and reduce the number of variable states, a new model of the original system is proposed. This model is too simple and is suitable to cognitive approach such as fuzzy modeling. Then, fuzzy modeling of an uncertain system using the approach of Ben-Ghalia et al. to reduce the effects of imperfections of the classical modeling are introduced. In addition, their applications in the fuzzy sliding mode control of the asynchronous motor are presented. Finally, Simulation results reveal some very interesting features and show that the proposed fuzzy model has great potential for use as an alternative to the approximation of the conventional model of induction motor taking into account the effect of system model uncertainties and gives a good performances in sliding mode control.