The possibility is studied of reducing the stabilization problem for delay differential nonlinear system to optimization problems with known numerical procedures for solving. Assuming a triangular structure of the system, algorithms are proposed for constructing a stabilizing control. The description of the subsystems in the form of Takagi–Sugeno models is used. Given the state and control constraints, as well as the properties of weight functions, the stabilization problem is reduced to some optimization problems, including LMIs. The obtained controls retain stabilizing properties for non-stationary weight functions, as well as for perturbed systems. Chances of numerical implementation of algorithms based on standard procedures of computational software are considered.

This paper describes a generalization of a method used for precision calibration of a strapdown INS. This method was proposed at the Laboratory of Control and Navigation and at the Department of Applied Mechanics and Control, Lomonosov Moscow State University. The method is practically used in specific applications. The purpose of a strapdown INS calibration is to determine the parameters of instrument errors of inertial sensors: accelerometers and gyros (angular rate sensors) to provide compensation in INS navigation mode. It is assumed that the assembled strapdown INS is located on the platform of a test bench. Test bench performs a set of rotations, the choice of which is part of the calibration task. The main source of data used for calibration are the readings of accelerometers and gyros themselves. Two modifications of the proposed method are described. In the first modification, only data from the accelerometers and gyros are used; in the second modification, the angular data provided by the test bench are also used. The estimation algorithms used are Kalman-type filtering algorithms.

The airborne gravity measurements both in Russia and abroad widely use the GT-2A aerogravimetric complex. This complex has a number of benefits but suffers from a serious limitation: in high latitudes, it is incapable of making measurements on westward courses. In this paper, we consider the causes of this drawback and propose theoretical solutions to fix it. Based on the obtained extensive empirical data, we select the most suitable solution. This enables us to suggest a modification of the GT-2A gravimetric complex for conducting airborne gravity surveys in the regions of the polar caps of the Earth.

The linear discrete minimum-phase plant with one control input, one measured output and with an unmeasured external disturbance is considered. The problem is stated of the design of the discrete output controller that provides the preset engineering performance indices: control error, settling time, stability margins radius. Analytical formulas are obtained that allow to relate the engineering performance indices with the desired closed system characteristic polynomial roots in the modal control problem when choosing real non-negative roots. At the same time, the specified control error and the settling time lead to the constraints on the maximum absolute value of the desired roots, while the values of the desired roots, providing the given stability margins radius, may not satisfy these constraints, so the specified values of the performance indices should be revised. Examples are given showing the effectiveness of the approach proposed.

An application of a quantizer–dequantizer method as a unifying description for representations of states in quantum mechanics is considered. Well-known quasi-distributions and tomograms are rewritten in terms of the dequantizer and quantizer operators. Using this description of the tomographic probability function and its symbol, we construct the invertible integral transforms between the tomogram and the quasi-probability distributions such as Wigner, Kirkwood–Rihaczek, Choi–Williams, P- and Q-functions, and others.