Subanalytic sets and feedback control
TLDR
The theory of subanalytic sets is used in this article to prove that analytic control systems are controllable, and that for every point p in the state space there exists a piecewise analytic feedback control that steers every state into p.About:
This article is published in Journal of Differential Equations.The article was published on 1979-01-01 and is currently open access. It has received 225 citations till now. The article focuses on the topics: State space & Piecewise.read more
Citations
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Asymptotic stability and feedback stabilization
TL;DR: In this paper, the authors considered the problem of determining when there exists a smooth function u(x) such that x = xo is an equilibrium point which is asymptotically stable.
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Smooth stabilization implies coprime factorization
TL;DR: In this paper, it was shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system.
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Developments in nonholonomic control problems
Ilya Kolmanovsky,N.H. McClamroch +1 more
TL;DR: Nonholonomic control systems as discussed by the authors provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole.
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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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Nonlinear regulation: The piecewise linear approach
TL;DR: In this paper, a discrete-time piecewise linear system with next-state and output maps described by affine linear maps is presented. Butler et al. showed that the results on state and output feedback, observers, and inverses, standard for linear systems, are also applicable to PL systems.
References
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Controllability of nonlinear systems
TL;DR: In this article, the controllability of nonlinear systems described by the equation dx/dt - F(x,u) was discussed and it was shown that strong accessibility implies strong accessibility for a large class of manifolds including Euclidean spaces.
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Linear differential systems with singularities and an application to transitive Lie algebras
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Stratification of Real Analytic Mappings and Images.
TL;DR: Hardt as mentioned in this paper showed that the image I of a semianalytic set under a proper analytic mapping of real analytic manifolds admits a locally-finite partition into connected submanifolds P such that QcClosP and dimQ