Numerical Solution of Algebraic Riccati Equations
This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way. Some proofs of theoretical results are simplified and a unified notation is adopted. The book includes a unified discussion of doubling algorithms and a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations and their MATLAB??codes. This will help the reader to gain an understanding of the computational issues and provide ready-to-use implementation of the different solution techniques. Ideal for researchers working in the design and analysis of algorithms and for practitioners who need to understand the available algorithms and software.
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A. J. Laub ADI iteration affine transform algebraic Riccati equations applied approximation Aſº Assume Benner block BXmin c-antistable c-splitting c-stabilizing solution Cayley transform Cited Cm×n Cn×n columns computation continuous-time Control convergence DARE defined deflating subspace discrete-time eigenvalues of A(z eigenvalues of H eigenvector exists following result Fréchet derivative GCARE Hamiltonian matrix Hermitian solution invariant subspace Jordan chains k—xco kmax Krylov subspace Linear Algebra Appl Lyapunov equation M-matrix M-NARE Matrix Anal matrix coefficients matrix H matrix pencil matrix sign function Mehrmann Meini minimal nonnegative solution Moreover NARE Newton’s iteration Newton’s method norm obtained orthogonal problem Proof properties PVL form QR algorithm QR factorization Schur complement Schur decomposition Section sequence shift technique SIAM sign function singular irreducible solution Xmin solving algebraic Riccati stability step structure Sylvester equation symplectic matrix unique UQME vector view of Theorem zero