## A Unified Algebraic Approach To Control DesignThis text deals with the most fundamental deficiency of modern theory control: the lack of an easily applicable method for the design of low order controllers. It shows that solutions to many different problems in control all reduce to the same linear algebra problem. It employs matrix equalities and matrix inequalities in the solutions of fixed order control and also provides computational algorithms. |

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### Contents

Introduction | 1 |

Summary | 9 |

Summary | 32 |

Summary | 49 |

Covariance Controllers | 89 |

Covariance Upper Bound Controllers | 131 |

Tix Controllers | 157 |

Model Reduction | 175 |

### Common terms and phrases

analytic center arbitrary matrix assumption asymptotically stable bound control problem chapter closed-loop system computational constraint sets continuous-time control design problems control input convergence convex sets Corollary covariance bound covariance matrix covariance upper bound defined discrete-time discrete-time system dynamic output feedback eigenvalues exists a controller exists a matrix feasibility problem feedback gain following statements full-order guaranteed Hence holds iteration Lemma linear algebra linear matrix inequality linear systems linear time-invariant Lyapunov equation Lyapunov function Lyapunov matrix matrix inequality matrix pair model reduction problem norm Note optimization problem orthogonal matrix orthogonal projection output covariance output feedback controller parametrization performance bound performance measure positive definite matrix quadratic Riccati equation satisfying scalar Schur complement formula second-order information singular value decomposition skew-Hermitian matrix solution space stabilizable stabilizes the system statements are equivalent static output feedback subspace Suppose symmetric matrix uncertain system uncertainty vector XY-centering Algorithm

### Popular passages

Page 278 - Guaranteed Asymptotic Stability for Some Linear Systems with Bounded Uncertainties, " ASME Journal of Dynamic Systems.

### References to this book

A Course in Robust Control Theory: A Convex Approach Geir E. Dullerud,Fernando Paganini No preview available - 2005 |

Advances in Linear Matrix Inequality Methods in Control Laurent El Ghaoui,Silviu-Iulian Niculescu No preview available - 2000 |