Constructive nonsmooth stabilization of triangular systems

Čelikovský, Sergej; Aranda-Bricaire, E.

doi:10.1016/s0167-6911(98)00062-0

Cited by 75 publications

(58 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Usually, these nonlinear systems are hard to control effectively, and their variety makes it even harder to obtain a unified method of stabilization. Here, we will only consider a well-known system, but the proposed design idea may also be applicable to generalized systems with similar structures (such as those studied in [12]). …”

Section: Classmentioning

confidence: 99%

A New Approach to Terminal Sliding Mode Control Design

Ye¹,

Yang

Cheng³

et al. 2008

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

Section: Classmentioning

confidence: 99%

A New Approach to Terminal Sliding Mode Control Design

Ye¹,

Yang

Cheng³

et al. 2008

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…Here f is homogeneous with respect to the dilation r = (1, 2) (cf. [4] and so it is natural to seek a CLF which is also homogeneous with respect to the dilation r = (1, 2)S. Consider the continuously differentiable CLF candidate…”

Section: Examplementioning

confidence: 99%

“…Since α is homogeneous of degree 6 with respect to the dilation r = (1, 2) and the compact n− sphere is compact, the standard arguments can be used to establish that, for some k, we have α(ξ) ≥ 0 for all ξ (cf. [4]). We set w = w k .…”

Section: Examplementioning

confidence: 99%

Lower Bounded Control-Lyapunov Functions

Hirschorn¹

2008

Communications in Information and Systems

View full text Add to dashboard Cite

Abstract. The well known Brockett condition -a topological obstruction to the existence of smooth stabilizing feedback laws -has engendered a large body of work on discontinuous feedback stabilization. The purpose of this paper is to introduce a class of control-Lyapunov function from which it is possible to specify a (possibly discontinuous) stabilizing feedback law. For control-affine systems with unbounded controls Sontag has described a Lyapunov pair which gives rise to an explicit stabilizing feedback law smooth away from the origin -Sontag's "universal construction" of Artstein's Theorem. In this work we introduce the more general "lower bounded control-Lyapunov function" and a "universal formula" for nonaffine systems. Our "universal formula" is a static state feedback which is measurable and locally bounded but possibly discontinuous. Thus, for the corresponding closed loop system, the classical notion of solution need not apply. To deal with this situation we use the generalized solution due to Filippov.

show abstract

“…Evidently, the ability to operate a sliding mode process in an optimal manner remains a challenging task as the computational complexity associated with such problems often proves to be a bottleneck [7]. Some constructive implementable algorithms for numerical treatment of switched/hybrid systems are discussed in [5,16,44]. This paper is an extended version of the previous conference presentation [11].…”

Section: Introductionmentioning

confidence: 99%