A Unified Algebraic Approach To Control Design
CRC Press, Oct 17, 1997 - Technology & Engineering - 304 pages
This 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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Covariance Upper Bound Controllers
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
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