Related papers: A tunable mixed feedback oscillator
We present a design framework to induce stable oscillations through mixed feedback control. We provide conditions on the feedback gain and on the balance between positive and negative feedback contributions to guarantee robust oscillations.…
We study the problem of controlling oscillations in closed loop by combining positive and negative feedback in a mixed configuration. We develop a complete design procedure to set the relative strength of the two feedback loops to achieve…
Feedback loops are major components of biochemical systems. Many systems show multiple such (positive or negative) feedback loops. Nevertheless, very few quantitative analyses address the question how such multiple feedback loops evolved.…
Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein…
This paper investigates the robustness of the Lur'e problem under positivity constraints, drawing on results from the positive Aizerman conjecture and robustness properties of Metzler matrices. Specifically, we consider a control system of…
We propose a new analog feedback controller based on the classical cross coupled electronic oscillator. The goal is to drive a linear passive plant into oscillations. We model the circuit as Lur'e system and we derive a new graphical…
The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper…
The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for…
Biomolecular feedback systems are now a central application area of interest within control theory. While classical control techniques provide invaluable insight into the function and design of both natural and synthetic biomolecular…
The paper is devoted to a design of a common bounded feedback control steering a system of an arbitrary number of linear oscillators to the equilibrium. At high energies, the control is based on the asymptotic theory of reachable sets of…
It is known that the stability of a feedback interconnection of two linear time-invariant systems implies that the graphs of the open-loop systems are quadratically separated. This separation is defined by an object known as the multiplier.…
Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular calcium release. Recent studies with simplified models have identified two advantages of…
Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits have been…
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…
Spikes and rhythms organize control and communication in the animal world, in contrast to the bits and clocks of digital technology. As continuous-time signals that can be counted, spikes have a mixed nature. This paper reviews ongoing…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…
The paper introduces notions of robustness margins geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and in engineering, a theory of robustness for behaviors away from…
This paper presents a new design framework for dynamic output-feedback controllers for Lur'e oscillation in a multiple-input multiple-output setting. We first revisit and extend dominant system theory to state-dependent rates, with the goal…
This note studies the exponential convergence of input-output signals of discrete-time nonlinear systems composed of a feedback interconnection of a linear time-invariant system and a nonlinear uncertainty. Both the open-loop subsystems are…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…