Spectral conditions for symmetric positive real and negative imaginary systems

Bajçinca, Naim; Voigt, Matthias

doi:10.23919/ecc.2013.6669824

Cited by 8 publications

(4 citation statements)

References 16 publications

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“…Notice that this concept of WSNI is only defined for the rational case. It coincides, in the symmetric case, to the concept of "strictly negative imaginary system" used in [27]. The following two examples show that conditions (iii) and (iv) in Theorem 3 are not implied by the first two, i.e., the notion of WSNI is indeed a weaker notion than that of SSNI.…”

Section: B Weakly Strictly Negative Imaginary Systemsmentioning

confidence: 55%

Foundations of Not Necessarily Rational Negative Imaginary Systems Theory: Relations Between Classes of Negative Imaginary and Positive Real Systems

Ferrante

Lanzon

Ntogramatzidis

2016

IEEE Trans. Automat. Contr.

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In this paper we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory. In analogy with the theory of positive real functions, in our general framework negative imaginary systems are defined in terms of a domain of analyticity of the transfer function and of a sign condition that must be satisfied in such domain. In this way, we do not require to restrict the attention to systems with a rational transfer function. In this work, we also define various grades of negative imaginary systems and aim to provide a unitary view of the different notions that have appeared so far in the literature within the framework of positive real and in the more recent theory of negative imaginary systems, and to show how these notions are characterized and linked to each other.

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Section: B Weakly Strictly Negative Imaginary Systemsmentioning

confidence: 55%

Foundations of Not Necessarily Rational Negative Imaginary Systems Theory: Relations Between Classes of Negative Imaginary and Positive Real Systems

Ferrante

Lanzon

Ntogramatzidis

2016

IEEE Trans. Automat. Contr.

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“…Stability analyses for interconnected NI systems with different approaches are presented in [5,11,13,14,[19][20][21][22][23][24][25][26]. Spectral conditions for NI systems with application to nano-positioning were presented in [27][28][29]. A feedback control utilizing NI controller for vibration control was introduced by [8,30].…”

Section: Open Loop Closed Loop 48dbmentioning

confidence: 99%

Stability Analysis and Vibration Control of a Class of Negative Imaginary Systems

et al. 2015

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This paper presents stability analysis and vibration control of a class of negative imaginary systems. A flexible manipulator that moves in a horizontal plane is considered and is modelled using the finite element method. The system with two poles at the origin is shown to possess negative imaginary properties. Subsequently, an integral resonant controller (IRC) which is a strictly negative imaginary controller is designed for the position and vibration control of the system. Using the IRC, the closed-loop system is observed to be internally stable and simuation results show that satisfactory hub angle response is achieved. Furthermore, vibration magnitudes at the resonance modes are suppressed by 48 dB.

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“…Furthermore, if the system represented by G(s) is externally passive, then it admits an internally passive minimal realization satisfying (3.67). To see the broad aspect and diverse applications of symmetric systems one can refer to [33][34][35][36][37][38]. The symmetric characteristic of transfer function as explored in Lemma 3.2.2 can be illustrated through the model of a space structure with collocated sensors and actuators [51] described by…”

Section: Symmetric Systemsmentioning

confidence: 99%

“…Frequently, such systems admit a positivity constraint as well which makes their stability and control problem even more challenging. A great deal of effort was devoted at early stage of system development to understand the concepts of symmetry and passivity [33][34][35][36][37][38]. Although both positive and symmetric systems have been tackled separately and employed in system theory, the combined presence of them in control application has not been thoroughly investigated.…”

Section: Introductionmentioning

confidence: 99%

Stabilization, estimation and control of linear dynamical systems with positivity and symmetry constraints

Oghbaee¹

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Bahram Shafai. I am deeply indebted to him not only for his fundamental role in my doctoral work, but also for every bit of guidance, expertise, and assistance that he selflessly provided. He gave me the freedom to examine a wider scope of research interests and contributed with most vital feedback, insights, and encouragements. I especially benefited from his expertise and knowledge to explore new directions and solve challenging problems. During the most difficult times of writing this dissertation, he gave me the moral support and the freedom I needed to make progress. It has been an honor to be his Ph.D. student. I gratefully acknowledge the members of my Ph.D. committee, Professor Mario Sznaier, Professor Rifat Sipahi, and Professor Mikhail Malioutov for their time and valuable feedback on preliminary version of this dissertation. I also highly appreciate their flexibility in dedicating their precious time for serving in my Ph.D. committee. I can never find enough words to describe how grateful I am for all of the supports my family provided for me in every part of my life. I am deeply thankful to my father for his support and guidance throughout my entire life. I am also grateful to my beloved mother whose emotional support and encouragements cherished me all these years. I also like to thank my sister for her love, encouragement, and empathy. Finally, my utmost love and appreciation goes to my dear wife, Shima,

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Spectral conditions for symmetric positive real and negative imaginary systems

Cited by 8 publications

References 16 publications

Foundations of Not Necessarily Rational Negative Imaginary Systems Theory: Relations Between Classes of Negative Imaginary and Positive Real Systems

Foundations of Not Necessarily Rational Negative Imaginary Systems Theory: Relations Between Classes of Negative Imaginary and Positive Real Systems

Stability Analysis and Vibration Control of a Class of Negative Imaginary Systems

Stabilization, estimation and control of linear dynamical systems with positivity and symmetry constraints

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