Coprime fractional representations of nonlinear systems

Verma, M.S.

doi:10.1109/iscas.1988.15438

Cited by 15 publications

(24 citation statements)

References 13 publications

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“…Further, given a system {G*, K * } with skr R { G * , K * } : ( U , y) H ZG*K* which is well posed and stable over BG*K*, there exist "stable" kernel representations for the systems S* and Q* given by (20) and (21), respectively, such that Gs. = G* and KQ* = K*, and the system ( S * , Q*} is well posed and stable over…”

Section: Remark 33mentioning

confidence: 99%

“…If {G, K } is generally stable, then (20) and (21) give skr's for S* and Q*, and the set in parenthesis in (25) will be empty. (24) …”

Section: Remark 33mentioning

confidence: 99%

“…If {G, K } is generally stable, then by Theorem 3.1, (20) and ( Remark 3.7: Note that the apparent discrepancy between (24) and (25) is due to the fact that (20) and (21) do not necessarily give stable kernel representations for S* and &*.…”

Section: [Rtz::i;}]-'zg*j~ Is Stable and By Stability Of The Kernementioning

confidence: 99%

“…Right and left factorizations have been previously defined both in terms of Bezout identities; see for example [20], [l], and [2], and from a set theoretic point of view, see [13], [5], and [9]. In the linear case these definitions are equivalent, and in the nonlinear case these definitions may be seen to be equivalent for right coprime factorizations.…”

Section: Proposition 42mentioning

confidence: 99%

“…Other work has been conducted attempting to derive a right factorization based approach to these results, notably the work by Verma [20]- [22]; see also the work by Chen [l], [ 2 ] . A general Youla parameterization using this approach has not been derived.…”

Section: Introductionmentioning

confidence: 99%

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The class of stabilizing nonlinear plant controller pairs

Paice

Schaft

1996

IEEE Trans. Automat. Contr.

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Abstract-In this paper a general approach is taken to yield a characterization of the class of stable plant controller pairs which is a generalization of the Youla parameterization for linear systems. This is based on the idea of representing the input-output pairs of the plant and controller as elements of the kernel of some related operator which is denoted the kernel representation of the system. It is demonstrated that in some sense the kernel representation is a generalization of the left coprime factorization of a general nonlinear system. Results giving one method of deriving a kernel representation for a nonlinear plant with a general state-space description are presented.

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Section: Remark 33mentioning

confidence: 99%

“…If {G, K } is generally stable, then (20) and (21) give skr's for S* and Q*, and the set in parenthesis in (25) will be empty. (24) …”

Section: Remark 33mentioning

confidence: 99%

Section: [Rtz::i;}]-'zg*j~ Is Stable and By Stability Of The Kernementioning

confidence: 99%

Section: Proposition 42mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The class of stabilizing nonlinear plant controller pairs

Paice

Schaft

1996

IEEE Trans. Automat. Contr.

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Robust stabilisation of nonlinear plants via left coprime factorizations

Paice

Moore

1990

Systems & Control Letters

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Stability of non-linear QFT designs based on robust absolute stability criteria

Baños¹,

Barreiro²

2000

International Journal of Control

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S tability of non-linear QFT designs based on robust absolute stability criteria ALFONSO BAN Ä OS{ and ANTONIO BARREIRO{The paper is mainly devoted to the robust stability problem of non-linear QFT designs. The problem is ® rst formulated for SISO non-linear systems, limited in practice to linear-memoryless sector-bounded non-linear interconnections, and in an I/O stability sense. The work investigates several possible robust adaptations of the Circle Criterion, depending on the type of resulting interconnection of linear and non-linear blocks, appearing in the feedback system. Also, the use of the Popov Criterion is investigated as an alternative less conservative than the Circle Criterion in some cases. The proposed techniques are given in usual QFT language, expressed as frequency conditions or boundaries in the Nichols Chart, allowing an easy integration with other design objectives. In addition, multivariable extensions using a conicity condition and the concept of maximal cone are adopted to give stability boundaries in interconnections of SIMO linear± MISO sector-bounded memoryless blocks. All the robust stability criteria are illustrated using signi® cant examples to emphasize the practical application of the resulting techniques.

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Coprime fractional representations of nonlinear systems

Cited by 15 publications

References 13 publications

The class of stabilizing nonlinear plant controller pairs

The class of stabilizing nonlinear plant controller pairs

Robust stabilisation of nonlinear plants via left coprime factorizations

Stability of non-linear QFT designs based on robust absolute stability criteria

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