Journal ArticleDOI
Dither in nonlinear systems
George Zames,N. Shneydor +1 more
TLDR
In this article, it was shown that the stability of a dither system is related to that of an equivalent smoothed system, whose nonlinear element is the convolution of the dither distribution and the original nonlinearity.Abstract:
A dither is a high-frequency signal introduced into a nonlinear system with the object of augmenting stability. In this paper,[1] it is shown that the effects of dither depend on its amplitude distribution function. The stability of a dithered system is related to that of an equivalent smoothed system, whose nonlinear element is the convolution of the dither distribution and the original nonlinearity. The ability of dithers to stabilize large classes of nonlinear systems is explained in terms of an effective narrowing of the nonlinear sector. A feature of the approach taken here is that a deterministic (i.e., strong) concept of stability is established under probabilistic (i.e., weak) assumptions on the dither.read more
Citations
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A survey of models, analysis tools and compensation methods for the control of machines with friction
TL;DR: This survey is the first to bring to the attention of the controls community the important contributions from the tribology, lubrication and physics literatures, and provides a set of models and tools for friction compensation which will be of value to both research and application engineers.
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Variable structure control of nonlinear multivariable systems: a tutorial
TL;DR: In this paper, the design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented.
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Stabilization with relaxed controls
TL;DR: In this paper, the authors examined the possibility of stabilizing one-dimensional systems with a continuous closed loop relaxed control and showed that the family of systems stabilizable with relaxed control is larger than the family stabilisable with ordinary controls, even if each state can be driven asymptotically to the origin.
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Control of chaos: Methods and applications in engineering
TL;DR: A survey of the emerging field termed “control of chaos” is given, which includes traditional control engineering methods including linear, nonlinear and adaptive control, neural networks and fuzzy control, and applications in various fields of engineering.
Journal ArticleDOI
Control of Chaos: Methods and Applications. I. Methods
TL;DR: The problems and methods of control of chaos, which in the last decade was the subject of intensive studies, were reviewed and the basic results obtained within the framework of the traditional linear, nonlinear, and adaptive control, as well as the neural network systems and fuzzy systems were presented.
References
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Journal ArticleDOI
On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity
TL;DR: In this article, the authors outline a stability theory for input-output problems using functional methods and derive open loop conditions for the boundedness and continuity of feedback systems, without, at the beginning, placing restrictions on linearity or time invariance.
Journal ArticleDOI
On the input-output stability of time-varying nonlinear feedback systems--Part II: Conditions involving circles in the frequency plane and sector nonlinearities
TL;DR: In this paper, the authors outline a stability theory based on functional methods and derive several stability conditions, including Popov's condition, under various restrictions on the nonlinearity N ; the following cases are treated: (i) N is instantaneously inside a sector and is memoryless and time-invariant.