TECHNICAL STABILITY OF NONSTATIONARY AUTOMATIC-CONTROL SYSTEMS WITH VARIABLE STRUCTURE

摘要

Sufficient conditions of technical stability in measure are established for nonstationary automatic-control systems with variable structure and logic control laws dependent on the mismatch error and its derivatives of finite order for all admissible initial perturbations from a predefined measurable set of initial perturbations. The associated systems of differential equations contain time-dependent coefficients. The logic control laws are described by a variable jump control function of the mismatch coordinate and its derivatives of finite order that is no higher than that of the initial system of equations. Using a signal and its derivatives for control increases the quality of discontinuous control. The relationship between the eigenvalues of the quadratic forms of the corresponding Liapunov functions and the criteria of technical stability is revealed. The general results are applied to a variable-structure system of the third order.