Numerical methods for linear control systems: design and by Biswa Nath Datta

By Biswa Nath Datta

Numerical equipment for Linear keep watch over platforms layout and research is an interdisciplinary textbook geared toward systematic descriptions and implementations of numerically-viable algorithms according to well-established, effective and strong sleek numerical linear recommendations for mathematical difficulties bobbing up within the layout and research of linear regulate platforms either for the 1st- and second-order versions. MATLAB-based software program is integrated for enforcing the entire significant algorithms from the e-book. * specified assurance of recent mathematical suggestions equivalent to parallel computations, second-order structures, and large-scale options* history fabric in linear algebra, numerical linear algebra, and keep an eye on concept integrated in textual content* step by step causes of the algorithms and examples* contains MATLAB-based resolution software program

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Extra info for Numerical methods for linear control systems: design and analysis (Final draft, March 10, 2003)

Example text

6 Similar Matrices . . . . . . . . . . . . . . . 7 Orthogonal Projection . . . . . . . . . . . . . . 41 Some Special Matrices . . . . . . . . . . . . . . 1 Diagonal and Triangular Matrices . . . . . . . . . . 2 Unitary (Orthogonal) Matrix . . . . . . . . . . . . 3 Permutation Matrix . . . . . . . . . . . . . . 4 Hessenberg (Almost Triangular) Matrix . . . . . . . . . 5 Companion Matrix . .

5 Companion Matrix . . . . . . . . . . . . . . 6 Nonderogatory Matrix . . . . . . . . . . . . . 7 The Jordan Canonical Form of a Matrix . . . . . . . . . 8 Positive Definite Matrix . . . . . . . . . . . . . 9 Block Matrices . . . . . . . . . . . . . . . . 46 Vector and Matrix Norms . . . . . . . . . . . . . 1 Vector Norms . . . . . . . . . . . . . . . . 2 Matrix Norms . . . . . . . . . . . . . .

It has only one eigenvector 1 . 2 Range and Nullspaces For every m × n matrix A, there are two important associated subspaces: the range of A, denoted by R(A), and the null space of A, denoted by N (A), defined as follows: R(A) = {b | b = Ax for some x} N (A) = {x | Ax = 0}. The dimension of N (A) is called the nullity of A and is denoted by null(A). 3 Rank of a Matrix Let A be an m × n matrix. Then the subspace spanned by the row vectors of A is called the row space of A. The subspace spanned by the columns of A is called the column space of A.

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