The aim of the study is to construct a suboptimal controller with the -criterion that stabilizes the deviation of the dynamic system from the given program trajectory. It is assumed that an impulse disturbance will be applied to one input of the system, and an -disturbance to the second one. The -norm is equal to the maximum value of the -output norm for all - and impulse disturbances vectors for which the sum of the quadratic form of the impulse disturbance vector with a given weight matrix and the squared -norm of the second disturbance never greater than one. In this paper, it is required to demonstrate the process of calculating the -norm in terms of linear matrix inequalities for a dynamical system and a system with uncertainty. An important role in the process of combining the -norm and the -norm in the -norm is played by the weight matrix included in the definition of this norm. It should be noted that, unlike the -norm, the -norm is achieved in the sense of the worst - and impulse disturbances, where the maximum value of the -output norm is reached. It is necessary to obtain and linearize the mathematical model of the quadcopter, build a programmed trajectory, and stabilize the deviations using a suboptimal control law with the - criterion in the presence of noise in the system. Linear matrix inequalities are used for suboptimal control searching. The object of this study is a quadcopter, which is an unmanned aerial vehicle with four engines with propellers that create thrust. The axes of the propellers and the angles of the blades are fixed and only the speed of rotation is regulated, which greatly simplifies the design. Using the Newton- Euler equation, a nonlinear mathematical model of a quadcopter is obtained, and this model is linearized. In the MATLAB environment, using the applied package for modeling and optimization YALMIP, Sedumi toolbox, numerical modeling, and construction of quadcopter motion trajectories are performed. After that, in the Simulink environment, a control block that stabilizes the movement of the quadcopter along a given trajectory in the presence of - and impulse disturbances in the system is constructed. At the end, a demonstration of the process of virtual visualization of the flight is made.
