Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems

Lin, Wei; Qian, Chunjiang

doi:10.1016/s0167-6911(99)00115-2

Cited by 527 publications

(350 citation statements)

References 20 publications

Supporting

Mentioning

347

Contrasting

Unclassified

Order By: Relevance

“…This has motivated many specific contributions, see Freeman and Kokotović, 1993;Kanellakopoulos et al, 1991;Krishnamurthy and Khorrami, 2006;Jiang et al, 2004;Lin and Qian, 2000) for instance.…”

Section: Discussionmentioning

confidence: 99%

A Unifying Point of View on Output Feedback Designs

Andrieu

Praly

2007

IFAC Proceedings Volumes

View full text Add to dashboard Cite

Abstract:Output feedback design for non linear systems is a difficult topic which has attracted the attention of researchers with very different approaches. We propose here a unifying point of view on possibly all these contributions. We start with a necessary condition on the structure of the Lyapunov functions for the closed loop system. This motivates the distinction of four classes of designs which can be placed in a two by two matrix (see Table 1), with -the direct approach, also called control error model analysis, and -the indirect approach, also called dynamic error model analysis, as entries in one direction, and domination and cancellation as entries in the other. We show how most available results on this topic can be reinterpreted along these lines.

show abstract

Section: Discussionmentioning

confidence: 99%

A Unifying Point of View on Output Feedback Designs

Andrieu

Praly

2007

IFAC Proceedings Volumes

View full text Add to dashboard Cite

show abstract

“…which violates the conditions used in [4,[11][12][13][14] due to x 1 and x 2 . However, in view of norm-bound, it is obvious that 1 3 ( , , ) | | t x u x δ ≤ which belongs to (9).…”

Section: [ ( ) ( )]mentioning

confidence: 94%

Adaptive Control of a Class of Feedforward and Non-feedforward Nonlinear Systems

Koo¹,

Choi²,

Lim³

2011

Journal of Institute of Control, Robotics and Systems

View full text Add to dashboard Cite

We propose a switching-based adaptive state feedback controller for a class of nonlinear systems that have uncertain nonlinearity. The base of the proposed conditions on the nonlinearity is the feedforward form, then it is extended via a nonlinear function containing all the states and the control input. As a result, more generalized systems containing feedforward and nonfeedforward terms are allowed as long as the ratio condition of the nonlinear function is satisfied. Moreover, the information on the growth rate of nonlinearity is not required a priori in our control scheme.

show abstract

“…The new approach is developed by using a basic concept of invariant manifold as well as an enhanced version of backstepping approach, namely adding a power integrator (Lin & Qian, 2000). The detailed derivation of the new output regulation approach consists of three steps described as follows:…”

Section: New Approach To Output Regulationmentioning

confidence: 99%

“…First, without resorting to any specific exosystems, the desired invariant manifold is solved and depicted by different time derivatives of both reference and disturbance signals. Second, to relaxing the assumption on sufficient smoothness of nonlinearities, the new output regulation law is developed via a feedback domination approach by means of the tool of adding a power integrator (Lin & Qian, 2000;Polendo & Qian, 2007). It is further dis-cussed that the finite time output regulation is achievable with some mild assumption on the homogeneous degree of the system.…”

Section: Introductionmentioning

confidence: 99%

Global output regulation for a class of lower triangular nonlinear systems: A feedback domination approach

Yang

Ding

2017

Automatica

View full text Add to dashboard Cite

An alternative but new nonlinear output regulation approach is proposed for a class of lower triangular nonlinear systems by using the tool of adding a power integrator. The invariant manifold is solved and represented in terms of various derivatives of disturbances and references. As such, it is unnecessary to suppose that the external disturbances being governed by certain exosystems anymore. The nonlinearities are not restricted to be sufficiently smooth due the the utilization of feedback domination approach. It is shown that the time taken to reach the desired invariant manifold from any initial states under external disturbances is guaranteed to be finite time. The control law is concise in structure for implementation since the feedback domination is implemented in each of the recursive design step.

show abstract

Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems

Cited by 527 publications

References 20 publications

A Unifying Point of View on Output Feedback Designs

A Unifying Point of View on Output Feedback Designs

Adaptive Control of a Class of Feedforward and Non-feedforward Nonlinear Systems

Global output regulation for a class of lower triangular nonlinear systems: A feedback domination approach

Contact Info

Product

Resources

About