ref_limits.bib

@article{freudenbergFundamentalDesignLimitations2003,
  title = {Fundamental Design Limitations of the General Control Configuration},
  author = {Freudenberg, J. S. and Hollot, C. V. and Middleton, R. H. and Toochinda, V.},
  year = {2003},
  month = aug,
  journal = {IEEE Transactions on Automatic Control},
  volume = {48},
  number = {8},
  pages = {1355--1370},
  issn = {1558-2523},
  doi = {10.1109/TAC.2003.815017},
  abstract = {The theory of fundamental design limitations is well understood for the case that the performance variable is measured for feedback. In the present paper, we extend the theory to systems for which the performance variable is not measured. We consider only the special case for which the performance and measured outputs and the control and exogenous inputs are all scalar signals. The results of the paper depend on the control architecture, specifically, on the location of the sensor relative to the performance output, and the actuator relative to the exogenous input. We show that there may exist a tradeoff between disturbance attenuation and stability robustness that is in addition to the tradeoffs that exist when the performance output is measured. We also develop a set of interpolation constraints that must be satisfied by the disturbance response at certain closed right half plane poles and zeros, and translate these constraints into generalizations of the Bode and Poisson sensitivity integrals. In the absence of problematic interpolation constraints we show that there exists a stabilizing control law that achieves arbitrarily small disturbance response. Depending on the system architecture, this control law will either be high gain feedback or a finite gain controller that depends explicitly on the plant model. We illustrate the results of this paper with the problem of active noise control in an acoustic duct.}
}

@article{freudenbergRightHalfPlane1985,
  title = {Right Half Plane Poles and Zeros and Design Tradeoffs in Feedback Systems},
  author = {Freudenberg, J. and Looze, D.},
  year = {1985},
  month = jun,
  journal = {IEEE Transactions on Automatic Control},
  volume = {30},
  number = {6},
  pages = {555--565},
  issn = {1558-2523},
  doi = {10.1109/TAC.1985.1104004},
  abstract = {This paper expresses limitations imposed by right half plane poles and zeros of the open-loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed-loop system. The limitations are determined by integral relationships which must be satisfied by these functions. The integral relationships are interpreted in the context of feedback design.}
}

@article{chenFundamentalLimitationsIntrinsic2019,
  title = {Fundamental Limitations and Intrinsic Limits of Feedback: {{An}} Overview in an Information Age},
  shorttitle = {Fundamental Limitations and Intrinsic Limits of Feedback},
  author = {Chen, Jie and Fang, Song and Ishii, Hideaki},
  year = {2019},
  month = jan,
  journal = {Annual Reviews in Control},
  volume = {47},
  pages = {155--177},
  issn = {1367-5788},
  doi = {10.1016/j.arcontrol.2019.03.011},
  url = {https://www.sciencedirect.com/science/article/pii/S1367578819300392},
  urldate = {2024-05-16},
  abstract = {This paper presents a review on the fundamental performance limitations and design tradeoffs of feedback control systems, ranging from classical performance tradeoff issues to the more recent information-theoretic analysis, and from conventional feedback systems to networked control systems, with an attempt to document some of the key achievements in more than seventy years of intellectual inquiries into control performance limitation studies, as so embodied by the timeless contributions of Bode known as the Bode integral relations.}
}

@article{chenSensitivityIntegralRelations1995,
  title = {Sensitivity Integral Relations and Design Trade-Offs in Linear Multivariable Feedback Systems},
  author = {Chen, Jie},
  year = {1995},
  journal = {Automatic Control, IEEE Transactions on},
  volume = {40},
  number = {10},
  pages = {1700--1716},
  issn = {0018-9286},
  doi = {10.1109/9.467680},
  abstract = {The purpose of this paper is to develop integral relations regarding the singular values of the sensitivity function in linear multivariable feedback systems. The main utility of these integrals is that they can be used to quantify the fundamental limitations in feedback design which arise due to system characteristics such as open-loop unstable poles and nonminimum phase zeros and to such fundamental design requirements as stability and bandwidth constraints. We present extensions to both the classical Bode sensitivity integral relation and Poisson integral formula. These extended integral relations exhibit important insights toward trade-offs that must be performed between sensitivity reduction and sensitivity increase due to the aforementioned system characteristics and design constraints. Most importantly, these results display new phenomena concerning design limitations in multivariable systems which have no analog in single-input single-output systems}
}

@article{chenSensitivityIntegralsMultivariable1995,
  title = {Sensitivity Integrals for Multivariable Discrete-Time Systems},
  author = {Chen, Jie and Nett, Carl N.},
  year = {1995},
  month = aug,
  journal = {Automatica},
  volume = {31},
  number = {8},
  pages = {1113--1124},
  issn = {0005-1098},
  doi = {10.1016/0005-1098(95)00032-R},
  url = {http://www.sciencedirect.com/science/article/B6V21-3YMFVGX-27/2/66cba6a90af2beff80d7fca28bb9d76a},
  urldate = {2011-02-17},
  abstract = {The purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete-time systems. We present extensions to both the classical Poisson integral and Bode's sensitivity integral formulae. The main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete-time systems, due to such system characteristics as open-loop unstable poles and nonminimum-phase zeros, and to such design requirements as stability and bandwidth constraints. These formulae are similar to those for multivariable continuous-time systems obtained elsewhere, and they reveal that feedback design limitations depend on directionality properties of the sensitivity function, and on those of unstable poles and nonminimum-phase zeros in the open loop transfer function.}
}

@article{jiechenSensitivityIntegralsTransformation1997,
  title = {Sensitivity Integrals and Transformation Techniques: A New Perspective},
  shorttitle = {Sensitivity Integrals and Transformation Techniques},
  author = {Jie Chen},
  year = {1997},
  journal = {Automatic Control, IEEE Transactions on},
  volume = {42},
  number = {7},
  pages = {1037--1044},
  issn = {0018-9286},
  doi = {10.1109/9.599991},
  abstract = {We provide alternative proofs for the classical Bode and Poisson-type sensitivity integrals and their extensions for both continuous-time and discrete-time systems. Our derivation uses the well-known properties of Laplace and Z transformations. This derivation helps establish a connection between Bode and Poisson-type sensitivity integrals and Laplace and Z transforms, hence providing an alternative perspective in interpreting these fundamental integral results}
}

@article{loozeLimitationsFeedbackProperties1991,
  title = {Limitations of Feedback Properties Imposed by Open-Loop Right Half Plane Poles},
  author = {Looze, D. P. and Freudenberg, J. S.},
  year = {1991},
  month = jun,
  journal = {IEEE Transactions on Automatic Control},
  volume = {36},
  number = {6},
  pages = {736--739},
  issn = {1558-2523},
  doi = {10.1109/9.86946},
  abstract = {An integral constraint on the closed-loop transfer function of unstable open-loop systems is used to quantify a tradeoff between feedback properties of the closed-loop system. This results in a lower bound on the peak of the complementary sensitivity function for unstable plants. The lower bound illustrates the nature of the tradeoff that is imposed, and provides insight into the difficulties imposed on the control of unstable systems. It can be used to quantitatively evaluate tradeoffs between the frequency of the open-loop unstable pole, the peak of the complementary sensitivity functions, and the bandwidth of the closed-loop system. Such a relationship has long been recognized, and is embodied in the classical design rule of thumb which states that the closed-loop bandwidth must be at least twice as large as the frequency of the unstable pole. Results which give insight into this rule and a theoretical basis for it are provided.{$<>$}}
}

@article{middletonTradeoffsLinearControl1991,
  title = {Trade-Offs in Linear Control System Design},
  author = {Middleton, R. H.},
  year = {1991},
  month = mar,
  journal = {Automatica},
  volume = {27},
  number = {2},
  pages = {281--292},
  issn = {0005-1098},
  doi = {10.1016/0005-1098(91)90077-F},
  url = {https://www.sciencedirect.com/science/article/pii/000510989190077F},
  urldate = {2021-04-29},
  abstract = {For some time now, many practitioners and researchers in the control area have been aware that unstable open loop poles, non-minimum phase zeros, and/or time delays make control systems design difficult. In this paper we examine the nature of these difficulties by discussing the results of Freudenberg and Looze (1987, 1988) and Sung and Hara (1988) on integral constraints on sensitivity functions. One of the key conclusions here is a set of rules of thumb, giving limitations on the closed loop bandwidth which are imposed by unstable open loop poles, non-minimum phase zeros and/or time delays.},
  langid = {english}
}

@article{qiuPerformanceLimitationsNonminimum1993,
  title = {Performance Limitations of Non-Minimum Phase Systems in the Servomechanism Problem},
  author = {Qiu, L. and Davison, E. J.},
  year = {1993},
  month = mar,
  journal = {Automatica},
  volume = {29},
  number = {2},
  pages = {337--349},
  issn = {0005-1098},
  doi = {10.1016/0005-1098(93)90127-F},
  url = {http://www.sciencedirect.com/science/article/pii/000510989390127F},
  urldate = {2014-05-10},
  abstract = {This paper studies the cheap regulator problem and the cheap servomechanism problem for systems which may be non-minimum phase. The study extends some well-known properties of ``perfect regulation'' and the ``perfect tracking and disturbance rejection'' of minimum phase systems to non-minimum phase systems. It is shown that perfect rejection to disturbances applied to the plant input can be achieved no matter whether the system is minimum phase or non-minimum phase, whereas a fundamental limitation exists in the achievable transient performance of tracking and rejection to disturbances applied to the plant output for a non-minimum phase system, and that this limitation can be simply and completely characterized by the number and locations of those zeros of the system which lie in the right half of the complex plane. Furthermore, this limitation provides a quantitative measure of the ``degree of difficulty'' which is inherent in the control of such non-minimum phase systems.}
}

@article{seronFeedbackLimitationsNonlinear1999,
  title = {Feedback Limitations in Nonlinear Systems: From {{Bode}} Integrals to Cheap Control},
  shorttitle = {Feedback Limitations in Nonlinear Systems},
  author = {Seron, M.M. and Braslavsky, J.H. and Kokotovic, P.V. and Mayne, D.Q.},
  year = {1999},
  month = apr,
  journal = {IEEE Transactions on Automatic Control},
  volume = {44},
  number = {4},
  pages = {829--833},
  issn = {0018-9286},
  doi = {10.1109/9.754828},
  abstract = {Feedback limitations of nonlinear systems are investigated using the cheap control approach. The main result is that in the limit, when the control effort is free, the smallest achievable L2 norm of the output is equal to the least amount of control energy (L2 norm) needed to stabilize the unstable zero dynamics. This nonlinear result is structurally similar to an earlier linear result by Qiu and Davison (1993), which, in turn, is connected with a Bode-type integral derived by Middleton (1991)}
}

@book{seronFundamentalLimitationsFiltering1997,
  title = {Fundamental {{Limitations}} in {{Filtering}} and {{Control}}},
  author = {Seron, Maria M. and Braslavsky, Julio H. and Goodwin, Graham C.},
  year = {1997},
  month = jan,
  series = {Communications and {{Control Engineering}}},
  publisher = {Springer},
  address = {London},
  url = {https://doi.org/10.1007/978-1-4471-0965-5},
  isbn = {3-540-76126-8}
}

@article{steinRespectUnstable2003,
  title = {Respect the Unstable},
  author = {Stein, G.},
  year = {2003},
  month = aug,
  journal = {IEEE Control Systems},
  volume = {23},
  number = {4},
  pages = {12--25},
  issn = {1066-033X},
  doi = {10.1109/MCS.2003.1213600},
  abstract = {Control engineers often design feedback control systems for inherently unstable systems, to keep them operating safely. In such cases, there are fundamental limitations on the achievable sensitivity function. The article discusses the potentially serious consequences of sensitivity constraints, input saturation, and instability. Inadequacies of control systems in such cases have led to deaths.}
}

@article{wuSimplifiedApproachBode1992,
  title = {A Simplified Approach to {{Bode}}'s Theorem for Continuous-Time and Discrete-Time Systems},
  author = {Wu, B.-F. and Jonckheere, E.A.},
  year = {1992},
  journal = {Automatic Control, IEEE Transactions on},
  volume = {37},
  number = {11},
  pages = {1797--1802},
  issn = {0018-9286},
  doi = {10.1109/9.173154},
  abstract = {A simplified approach to W.H. Bode's (1945) theorem for both continuous-time and discrete-time systems, along with some generalization, are presented. For continuous-time systems, the constraints of open-loop stability and roll-off at s={$\propto$} are removed. A counterexample shows that when the excess poles/zeros vanishes, the Bode integral drops from infinite to finite value when the open-loop gain crosses a critical value. A revised result is also developed. The salient feature of this approach is that at no stage are either Cauchy's theorem or the Poisson integral invoked; the simplified proof relies only on elementary analysis. This approach carries over to the discrete-time cases in a straightforward manner}
}