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Differentially passive circuits that switch and oscillate
The concept of passivity is central to analyze circuits as interconnections
of passive components. We illustrate that when used differentially, the same
concept leads to an interconnection theory for electrical circuits that switch
and oscillate as interconnections of passive components with operational
amplifiers (op-amps). The approach builds on recent results on dominance and
p-passivity aimed at generalizing dissipativity theory to the analysis of
non-equilibrium nonlinear systems. Our paper shows how those results apply to
basic and well-known nonlinear circuit architectures. They illustrate the
potential of dissipativity theory to design and analyze switching and
oscillating circuits quantitatively, very much like their linear counterparts
Robust stability conditions for feedback interconnections of distributed-parameter negative imaginary systems
Sufficient and necessary conditions for the stability of positive feedback
interconnections of negative imaginary systems are derived via an integral
quadratic constraint (IQC) approach. The IQC framework accommodates
distributed-parameter systems with irrational transfer function
representations, while generalising existing results in the literature and
allowing exploitation of flexibility at zero and infinite frequencies to reduce
conservatism in the analysis. The main results manifest the important property
that the negative imaginariness of systems gives rise to a certain form of IQCs
on positive frequencies that are bounded away from zero and infinity. Two
additional sets of IQCs on the DC and instantaneous gains of the systems are
shown to be sufficient and necessary for closed-loop stability along a homotopy
of systems.Comment: Submitted to Automatica, A preliminary version of this paper appeared
in the Proceedings of the 2015 European Control Conferenc
Brayton-Moser Equations and New Passivity Properties for Nonlinear Electro-Mechanical Systems
This paper presents an alternative framework for a practically relevant class of nonlinear electro-mechanical systems. The formalism is based on a generalization of Brayton and Moser’s mixed-potential function. Instead of focusing on the usual energy-balance, the models are constructed using the power flowing through the system. The main objective is to put forth the mixed-potential function as a new building block for modeling, analysis and controller design purposes for electro-mechanical systems
Monotone Control Systems
Monotone systems constitute one of the most important classes of dynamical
systems used in mathematical biology modeling.
The objective of this paper is to extend the notion of monotonicity to
systems with inputs and outputs, a necessary first step in trying to understand
interconnections, especially including feedback loops, built up out of monotone
components.
Basic definitions and theorems are provided, as well as an application to the
study of a model of one of the cell's most important subsystems.Comment: See http://www.math.rutgers.edu/~sontag/ for related wor
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