## Linear State-Space Control SystemsThe book blends readability and accessibility common to undergraduate control systems texts with the mathematical rigor necessary to form a solid theoretical foundation. Appendices cover linear algebra and provide a Matlab overivew and files. The reviewers pointed out that this is an ambitious project but one that will pay off because of the lack of good up-to-date textbooks in the area. |

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Having studied under both Professors Dr. Lawrence and Dr. Williams, I find this book to be very accessible as a reference after taken the appropriate modern control theory undergraduate and graduate classes. I would definitely recommend this book to any colleague with the appropriate background.

### Contents

StateSpace Fundamentals | 48 |

Controllability | 108 |

Observability | 149 |

Minimal Realizations | 185 |

Stability | 198 |

Asymptotic Stability | 220 |

Design of Linear State Feedback Control Laws | 234 |

Observers and ObserverBased Compensators | 300 |

Appendix B Linear Algebra | 417 |

Subspaces | 419 |

Standard Basis | 421 |

Change of Basis | 422 |

Orthogonality and Orthogonal Complements | 424 |

Linear Transformations | 426 |

Range and Null Space | 430 |

Eigenvalues Eigenvectors and Related Topics | 435 |

Introduction to Optimal Control | 357 |

Appendix A Matrix Introduction | 407 |

Matrix Arithmetic | 409 |

Determinants | 412 |

Matrix Inversion | 414 |

Norms for Vectors and Matrices | 444 |

Continuing MATLAB Example mﬁle | 447 |

456 | |

459 | |

### Common terms and phrases

algebraic associated asymptotically stable bounded-input bounded-output Bu(t canonical form realization Chapter characteristic polynomial closed-loop eigenvalues closed-loop state equation closed-loop system coefﬁcient matrices columns Compute Continuing Example Continuing MATLAB Example control law design controllability matrix controller canonical form coordinate transformation damping ratio deﬁned deﬁnition derive desired closed-loop desired eigenvalues diagonal canonical form differential equation eigenvalues eigenvector equation x(t equilibrium feedback control law ﬁrst ﬁrst-order given input signal linear quadratic regulator linear state equation linear time-invariant linear time-invariant system linearly independent Lyapunov Lyapunov stability MATLAB function matrix exponential minimal minimal realization multiple-input multiple-output nonsingular nonzero observer canonical form observer error observer gain observer-based compensator open-loop open-loop system pair A,B percent overshoot plot rank Riccati equation satisﬁes scalar second-order single-input single-output solution speciﬁed stability state-space realization step response system dynamics matrix system eigenvalues Theorem trajectory transfer function unit step response variables xi(t yields zero initial