## Optimization of Linear Control Systems: Analytical Methods and Computational AlgorithmsThe authors present analytical methods for synthesis of linear stationary and periodical optimal controlled systems, and create effective computational algorithms for synthesis of optimal regulators and filters. The procedures of Youla-Jabr-Bongiorno (1976) and Desoer-Lin-Murray-Saeks (1980) are special cases of this procedure. The monograph also includes original computational algorithms (solutions of usual and generalized Lyapunov and Riccati equations, polynomial matrix factorization) and illustrates the effectiveness of these algorithms by examples in the field of numerical methods for optimization of linear controlled systems. |

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### Contents

Linear Quadratic Problem | 11 |

Method of HOptimization Frequency Method of Synthesis | 59 |

Computing Algorithms of the State Space Method | 113 |

Computing Algorithms of the Frequency Method of Synthesis | 183 |

References | 247 |

Index | 259 |

### Common terms and phrases

according algebraic Riccati equation algorithm Aliev analog appropriate dimensions Arnold and Laub asymptotic asymptotically stable Bordyug calculation Cayley transformation closed system coincide condition control forces correlation corresponding defined desired matrix desired solution Desoer determined diag dimensions m x m Diophantine equation discrete eigenvalues ensures example expression frequency method GARE Hamiltonian matrix Hardi space Hurwitz Hurwitz polynomial imaginary axis initial invertible Kailath Kucera Larin left half-plane linear quadratic Lyapunov equation matrices mentioned matrix Q matrix signum function minimal Multiplying norm obtained optimal regulator orthogonal matrix orthogonal projector parametrization phase vector poles on C+ polynomial matrices problem of factorization quality criterion rational matrix reduced regulator equation relation result Riccati equation right half-plane satisfies scalar Schur method Sebryakov and Semenov Section sequence signum function singular solution of equation specified stabilizing solution Stage stationary symmetric matrix synthesis Theorem transfer function unit circle unit disk Youla zero