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   https://doi.org/10.1109/LCSYS.2024.3522944  

   Liu, Guanyun; Menezes, Amor A (December 2024, IEEE Control Systems Letters)

   Positive systems, which are systems whose states are always non-negative, can have both positive linear and positive nonlinear approximations that are valid dynamical models in a prescribed domain. When a linearization of a nonlinear system in a domain near an operating point is equivalent to another linear system representation, a reference-tracking controller for that linear system should also achieve reference-tracking control of the nonlinear system in that domain. Here, we show that only if a linearized positive nonlinear system (PNS) is a positive system (i.e., the PNS is cooperative) will a reference-tracking controller for an equivalent positive linear system realization achieve similar results on the nonlinear system. For an example noncooperative PNS of human blood coagulation, where a published reference-tracking controller assumed a positive linear plant, we develop feedforward and feedback controllers that augment the prior controller to overcome noncooperativity and similarly control the positive nonlinear model. 

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2. Magnetic Relaxation of a Voigt–MHD System

   https://doi.org/10.1007/s00220-023-04770-1  

   Constantin, Peter; Pasqualotto, Federico (September 2023, Communications in Mathematical Physics)
3. Minimax Persistent Monitoring of a network system

   https://doi.org/10.1016/j.automatica.2022.110808  

   Pinto, Samuel C.; Welikala, Shirantha; Andersson, Sean B.; Hendrickx, Julien M.; Cassandras, Christos G. (March 2023, Automatica)
4. Bilinear Controllability of a Simple Reparable System

   https://doi.org/10.23919/ECC64448.2024.10591269  

   Adu, Daniel Owusu; Hu, Weiwei (June 2024, IEEE)

   Reparable systems are systems that are characterized by their ability to undergo maintenance actions when failures occur. These systems are often described by transport equations, all coupled through an integro-differential equation. In this paper, we address the understudied aspect of the controllability of reparable systems. In particular, we focus on a two-state reparable system and our goal is to design a control strategy that enhances the system availability- the probability of being operational when needed. We establish bilinear controllability, demonstrating that appropriate control actions can manipulate system dynamics to achieve desired availability levels. We provide theoretical foundations and develop control strategies that leverage the bilinear structure of the equations. 

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5. A scale-dependent measure of system dimensionality

   https://doi.org/10.1016/j.patter.2022.100  

   Recanatesi, S.; Bradde, S.; Balasubramanian, V.; Steinmetz, N.; Shea-Brown, E. (January 2022, Patterns)

   A fundamental problem in science is uncovering the effective number of degrees of freedom in a complex system: its dimensionality. A system’s dimensionality depends on its spatiotemporal scale. Here, we introduce a scale-dependent generalization of a classic enumeration of latent variables, the participation ratio. We demonstrate how the scale-dependent participation ratio identifies the appropriate dimension at local, intermediate, and global scales in several systems such as the Lorenz attractor, hidden Markov models, and switching linear dynamical systems. We show analytically how, at different limiting scales, the scale-dependent participation ratio relates to well-established measures of dimensionality. This measure applied in neural population recordings across multiple brain areas and brain states shows fundamental trends in the dimensionality of neural activity—for example, in behaviorally engaged versus spontaneous states. Our novel method unifies widely used measures of dimensionality and applies broadly to multivariate data across several fields of science. 

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