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Control Systems Synthesis - A Factorization Approach, Part I (Paperback)
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Control Systems Synthesis - A Factorization Approach, Part I (Paperback)
Series: Synthesis Lectures on Control and Mechatronics
Expected to ship within 10 - 15 working days
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This book introduces the so-called ""stable factorization
approach"" to the synthesis of feedback controllers for linear
control systems. The key to this approach is to view the
multi-input, multi-output (MIMO) plant for which one wishes to
design a controller as a matrix over the fraction field F
associated with a commutative ring with identity, denoted by R,
which also has no divisors of zero. In this setting, the set of
single-input, single-output (SISO) stable control systems is
precisely the ring R, while the set of stable MIMO control systems
is the set of matrices whose elements all belong to R. The set of
unstable, meaning not necessarily stable, control systems is then
taken to be the field of fractions F associated with R in the SISO
case, and the set of matrices with elements in F in the MIMO case.
The central notion introduced in the book is that, in most
situations of practical interest, every matrix P whose elements
belong to F can be ""factored"" as a ""ratio"" of two matrices N,D
whose elements belong to R, in such a way that N,D are coprime. In
the familiar case where the ring R corresponds to the set of
bounded-input, bounded-output (BIBO)-stable rational transfer
functions, coprimeness is equivalent to two functions not having
any common zeros in the closed right half-plane including infinity.
However, the notion of coprimeness extends readily to discrete-time
systems, distributed-parameter systems in both the continuous- as
well as discrete-time domains, and to multi-dimensional systems.
Thus the stable factorization approach enables one to capture all
these situations within a common framework. The key result in the
stable factorization approach is the parametrization of all
controllers that stabilize a given plant. It is shown that the set
of all stabilizing controllers can be parametrized by a single
parameter R, whose elements all belong to R. Moreover, every
transfer matrix in the closed-loop system is an affine function of
the design parameter R. Thus problems of reliable stabilization,
disturbance rejection, robust stabilization etc. can all be
formulated in terms of choosing an appropriate R. This is a reprint
of the book Control System Synthesis: A Factorization Approach
originally published by M.I.T. Press in 1985. Table of Contents:
Introduction / Proper Stable Rational Functions / Scalar Systems:
An Introduction / Matrix Rings / Stabilization
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