## Stability in nonlinear control systems |

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### Contents

INTRODUCTION | 1 |

EQUATIONS OF CONTROL SYSTEMS STATEMENT OF STABILITY | 20 |

FIRST CANONICAL FORM OF EQUATIONS OF CONTROL SYSTEMS | 33 |

Copyright | |

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A. I. Lur'e A. M. Letov absolute stability accordance actuator ag+1 asymptotic stability automatic control bounded function calculate canonical equations canonical form canonical transformation Chapter characteristic number Chetaev coefficients Consequently constants control system coordinates curve denote determined disturbed motion disturbing forces first-approximation equations following form following theorem formulas function f(a Hurwitz inequalities hyperbola initial equations inverse transformation investigation Let us assume Let us consider limit linearized system Lur'e theorem Lyapunov function Lyapunov method n+1 n+1 Nonlinear obtain obvious solution parabola pi+1 Pn+1 positive definite function positive number possible proportional feedback quadratic equations quadratic form quantities real numbers real roots regulated object regulator parameters relations satisfy the condition second Bulgakov problem sign-definite simple roots solved specified stability conditions stability criterion Stability of Motion stability region steady subclass A1 sufficient conditions sufficiently small theory of automatic total derivative undisturbed values vanishes zero