Abstract
We derive sufficient conditions for the technical stability of forced states of automatic control systems with a variable structure depending on the derivatives of the control function. For arbitrary admissible initial perturbations from a measurable set of initial states of a control system with filtering, the technical stability conditions do not depend on the sliding conditions in the given domain of the system parameters. We find how the properties of the eigenvalues of the quadratic forms of the Lyapunov functions are related to the technical stability conditions for automatic control systems of variable structure with filtering. The technical stability conditions are analyzed for automatic control systems with third-order filtering where the forming signal creates eight structures
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