## Modern control theory |

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### Contents

Chapter 3 Matrix Algebra Derivation of Transfer Function 3 1 to 3 | 2-73 |

Chapter 4 Solution of State Equations 4 1 to 4 | 41 |

iapter5 Pole Placement Technique 5 1 to 5 | 5-1 |

Chapter6 Controllers 6 1 to 6 | 6-1 |

Review Questions 648 | 6-48 |

vii | 7-8 |

Chapter9 Liapunovs Stability Analysis 91 to 9 26 | 9-1 |

Important concepts are highlighted using key points throughout the book | 9-4 |

Examples with Solutions 912 | 9-12 |

Review Questions 9 24 | 9-24 |

5 Modern Control Theory | P-5 |

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A X(t asymptotically stable B U(s B U(t called canonical form characteristic polynomial closed loop poles cofactors completely observable completely state controllable constant control mode control system controllability matrix controller output damping ratio deadzone denominator desired characteristic equation Determine diagonal matrix differential equation eigen values eigen vectors equilibrium feedback controller feedback gain matrix frequency given system initial conditions input invariant system isocline Laplace transform Liapunov function Liapunov's function linear system modal matrix Modern Control Theory nonlinear system observer gain matrix obtained offset error partial fraction PD controller phase plane phase portrait phase trajectory phase variable form pole placement positive definite proportional controller Refer example Refer section response second order system shown si-A signal flow graph singular point Solution stability Substituting Sylvester's criterion system described system is completely theorem transfer function transition matrix unit step zero