Linear Multivariable Control: Algebraic Analysis and Synthesis MethodsDetails the basic theory of polynomial and fractional representation methods for algebraic analysis and synthesis of linear multivariable control systems. It also serves as a self-contained treatise of the mathematical theory so that results and techniques of the ``state space approaches'' for regular and singular systems appear as special cases of a general theory covering the wider class of PMDs of linear systems. Among the topics covered are: real rational vector spaces and rational matrices, pole and zero structure of rational matrices at infinity, proper and omega stable rational fuctions and matrices. |
Contents
Polynomial Matrix Models of Linear Multivariable Systems | 54 |
Pole and Zero Structure of Rational Matrices at Infinity | 91 |
Ts | 115 |
Copyright | |
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A₁ A₁(s A₂(s B₁ B₁(s B₂(s biproper rational column degrees column proper common left divisor Consider Control Corollary Cw(s D₁(s D₂(s decoupling zeros defined Definition deg d(s denote Diophantine equations equivalence relation Euclidean division Exercise exponentially feedback finite follows Hpol(s i.e. let IEEE Trans implies input internally proper invariant invariant polynomials Jâr Jordan pair Laplace transform left coprime Lemma Let T(s matrix differential equation minimal realization multivariable system N₁(s non-singular obtain P₁(s PMD A(p poles polynomial matrix polynomial MFD pr pr Proof proper rational matrix Proposition q₁ r₁ rank R(S rational functions rational matrix rational matrix T(s reachable Remark right coprime right divisor Rosenbrock row proper S-MFDs sâr satisfied Smith form Smith-McMillan form solution ST(s strictly proper system matrix T₁(s T₂(s TGL(S Theorem TL(s TR(S transfer function matrix unimodular matrix vector space zero structure