In this article, the stability of switched time-delay Persidskii systems is studied. Both cases of synchronous and asynchronous commutation are considered. A comparison of stability conditions obtained with the aid of Lyapunov-Razumikhin and Lyapunov-Krasovskii approaches is provided. The developed theory is applied to the stability analysis of mechanical systems with linear velocity forces and switched nonlinear positional ones.
A dynamically symmetric satellite in a circular orbit of small inclination is considered. The problem of the Lorentzian stabilization of the satellite in the orbital coordinate system in the indirect equilibrium position is solved under the conditions of the perturbing effect of the gravitational torque. To solve this problem, which is characterized by incomplete control, a method of averaging differential equations is developed. Using the original construction of the unsteady Lyapunov function, we obtain sufficient conditions for the asymptotic stability of the programmed satellite motion mode in the form of constructive inequalities with respect to the control parameters.
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