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When designing multidimensional optimal systems of information processing and control it is necessary to solve Wiener–Hopf matrix equations. The present article suggests a simple method for their solution.

A controller of an object that is designed in the space of states generally consists of two blocks: an observer and a block implementing a control law. The combination of the two blocks to form a unified block (modified controller) permits reducing the computational and the algorithmic complexity of processing the measurable information. Optimality criteria with small parameters are set up, which offer the possibility of designing a modified controller, leaving out the procedure of design of an observer.

A simple proof is given of the validity of one of the algorithms for solving the Wiener–Hopf equation.

Abstract: A one-dimensional object is used in considering control systems in state space or operator space. From the complexity viewpoint (number of sensors and number of elements in data-processing system), operator space is preferable, and certain tasks are more readily handled than in state space. Examples are given.

The internal friction and Young's modulus were determined from the damping of free bending vibrations at 0.2–5 kHz between 20 °C and 700 °C. The activation energy for the processes responsible for the appearance of the relaxation peaks was determined from the frequency shift of these peaks. The diffusion coefficient of Cu in Si was determined by the internal-friction method in this temperature range. The results found from the internal-friction measurements are compared with data from studies of electrical properties.

Construction standards are providing a number of measures to reduce deformations in the foundation bases and their influence on structures. These measures do not exclude a change in the spatial position of the structures, especially when it comes to significant uneven deformations. In connection with this, it is urgent to develop a method that allows supporting structures of buildings and structures in the design position with uneven local deformations of the ground base but with significant deformation occurrences accompanied by the tilts of the entire building and allowing to correct the geometric object position. The investigations carried out at this stage made it possible to develop a model range of spring-jack modules, produce experimental samples of spring-jack modules, obtain a picture of the work quality of the proposed technology.

Construction standards are providing a number of measures to reduce deformations in the foundation bases and their influence on structures. These measures do not exclude a change in the spatial position of the structures, especially when it comes to significant uneven deformations. In connection with this, it is urgent to develop a method that allows supporting structures of buildings and structures in the design position with uneven local deformations of the ground base but with significant deformation occurrences accompanied by the tilts of the entire building and allowing to correct the geometric object position. The investigations carried out at this stage made it possible to develop a model range of spring-jack modules, produce experimental samples of spring-jack modules, obtain a picture of the work quality of the proposed technology.