Journal ArticleDOI
Time domain and frequency domain conditions for strict positive realness
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The main theorem in this article can be considered as the positive realness lemma for strictly positive real systems and is clarified by means of a three-tier diagram; each tier represents a set of equivalent conditions successively stronger than the lower tier.Abstract:
The author states various time-domain and frequency-domain conditions pertaining to multivariate strict positive real systems and establishes the relationship between these conditions. Their relationship is clarified by means of a three-tier diagram; each tier represents a set of equivalent conditions successively stronger than the lower tier. The main theorem in the present study can be considered as the positive realness lemma for strictly positive real systems. >read more
Citations
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Linear Matrix Inequalities in System and Control Theory
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Survey Constructive nonlinear control: a historical perspective
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Controlled and conditioned invariants in linear system theory
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Solution to the positive real control problem for linear time-invariant systems
TL;DR: In this paper, the problem of synthesizing an internally stabilizing linear time-invariant controller for a linear time invariant plant such that a given closed-loop transfer function is extended strictly positive real was studied.
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Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete-time theory
TL;DR: In this paper, a Riccati-like matrix equation is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time-invariant system and a memoryless nonlinearity.
References
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Journal ArticleDOI
The stability of nonlinear dissipative systems
David J. Hill,P. Moylan +1 more
TL;DR: In this article, a technique for generating Lyapunov functions for a broad class of nonlinear systems represented by state equations is presented, where dissipativeness is characterized by the existence of a computable function which can be interpreted as the stored energy of the system.
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Frequency domain conditions for strictly positive real functions
Petros Ioannou,Gang Tao +1 more
TL;DR: In this article, the necessary and sufficient conditions in the frequency domain for transfer functions to be strictly positive real (SPR) functions are clarified further by giving necessary and necessary conditions in frequency domain.
Journal ArticleDOI
A simplified viewpoint of hyperstability
TL;DR: In this paper, the definition of a hyperstable system according to Popov is given a network theoretic interpretation, and proofs are presented outlining the connection between passive and hyperstable systems.
Journal ArticleDOI
On Frequency Domain Stability for Evolution Equations in Hilbert Spaces via the Algebraic Riccati Equation
TL;DR: In this paper, the authors established Lyapunov type stability for an evolution equation in a Hilbert space by using some energy functions which are obtained via the algebraic Riccati equation.