## The Autonomous Linear Quadratic Control Problem: Theory and Numerical SolutionA survey is given on the state of the art in theory and numerical solution of general autonomous linear quadratic optimal control problems (continuous and discrete) with differential algebraic equation constraints. It incorporates the newest developments on differential algebraic equations, Riccati equations and invariant subspace problems. In particular, it gives a decision chart of numerical methods, that can be used to determine the right numerical method according to special properties of the problem. The book closes a gap between mathematical theory, numerical solution and engineering application. The mathematical tools are kept as basic as possible in order to address the different groups of readers, mathematicians and engineers. |

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### Contents

Part | 1 |

Theoretical results | 15 |

Uniqueness and stability of feedback solutions | 39 |

Copyright | |

7 other sections not shown

### Common terms and phrases

algebraic Riccati equation analogous B*XE block boundary value problem Bunse-Gerstner Byers B 39 c-stable C'QC C*QC Cn,n columns complex compute condition number corresponding defect correction deflating subspace diagonal discrete e.g. Golub/Van Loan eigenvalues of modulus exists F G H F feedback flops following algorithm given Golub/Van Loan G Hamiltonian and symplectic Hamiltonian matrix Hessenberg form IEEE Trans invariant subspace invertible iteration Kronecker canonical form Laub Loan G 12 Lyapunov equation matrix pencils Mehrmann Newton's method nonsingular numerical methods obtain optimal control optimal control problems Paige/Van Loan perturbations positive definite positive semidefinite positive semidefinite solution problem 1.1 procedure PRoof QR-algorithm QR-decomposition real Hamiltonian real symplectic reduced Schur sign function singular value decomposition solve Step strongly detectable strongly stabilizable symplectic Hessenberg form symplectic matrices symplectic pencils Theorem theory unique unit circle upper Hessenberg upper triangular