## Mathematical methods for the study of automatic control systems |

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### Contents

Formulation of the problem of stability of motion Basic | 5 |

Investigation of Transient Processes in Linear Systems with | 70 |

Construction of Solutions for Nonlinear Systems of Dif | 145 |

Copyright | |

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### Common terms and phrases

almost-periodic approximation assume asymptotically stable automatic control system based on system behaviour characteristic values coefficients conditions of Theorem consider the system constantly acting perturbations construction continuous functions continuously differentiable convergence Corollary correlation functions curves of system defined denote differential equations estimate exist two functions exists a number follows form of series formula fundamental system homogeneous solution infinitely small upper initial conditions integral curve linear system Lyapunov function matrix members of system method necessary and sufficient negative-definite nonlinear parameters periodic solution polynomials positive constants positive number positive-definite positive-definite function possesses the property problem of stability Proof quadratic form region right-hand members satisfies the inequalities satisfying the conditions self-oscillation small upper bound solution of system stable with respect stochastic process substitution sufficiently small system of differential system of equations system of solutions total derivative transient processes trigonometric polynomials variable zero