## Short-time stability in linear time-varying systems |

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### Contents

Linear TimeVarying Systems Analysis | 7 |

ShortTime Stability in Undriven Systems | 21 |

ShortTime Stability in Driven Systems | 33 |

3 other sections not shown

### Common terms and phrases

2t I dT analog computer applied assure short-time asymptotically stable bound on y(t C-equivalent with respect Cascaded system Chzhan-sy-in Classical and short-time concept of short-time conditions for short-time determined driven stability f a(T feedback system finite time interval gain K(t given gmax impulse response w(t inequality inputs bounded instantaneous eigenvalue invariant systems linear systems linear time-varying systems loop impulse response Lyapunov matrix A(t maximum eigenvalue modified adjoint system necessary and sufficient obtain open loop impulse output bound output y(t phase space positive finite constant prescribed constant proof short-time C-equivalent short-time stability Solution stability in driven stability in feedback stable with respect step response study of short-time sufficient condition superposition integral system of Fig systems operating t t y(t Taylor series terms of w(t time-invariant system time-varying gain transfer function Uj(t undriven systems V(tQ Volterra integral equation w(tj w(tr Washington 25 y(tQ