Journal ArticleDOI
Small-gain theorem for ISS systems and applications
TLDR
This work addresses the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.Abstract:
We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the interest of these results, we address the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.read more
Citations
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Journal ArticleDOI
On characterizations of the input-to-state stability property
Eduardo D. Sontag,Yuan Wang +1 more
TL;DR: In this paper, the Lyapunov sufficient condition for "input-to-state stability" (ISS) is also shown to be necessary and sufficient, which is an open question raised by several authors.
Journal ArticleDOI
Input-to-state stability for discrete-time nonlinear systems
Zhong-Ping Jiang,Yuan Wang +1 more
TL;DR: The input-to-state stability property and small-gain theorems are introduced as the cornerstone of new stability criteria for discrete-time nonlinear systems.
Book ChapterDOI
Input to State Stability: Basic Concepts and Results
TL;DR: This expository presentation addresses the precise formulation of questions of robustness with respect to disturbances, formulated in the paradigm of input to state stability, with an intuitive and informal presentation of the main concepts.
Journal ArticleDOI
Necessary and sufficient graphical conditions for formation control of unicycles
TL;DR: It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node.
Journal ArticleDOI
New characterizations of input-to-state stability
Eduardo D. Sontag,Yuan Wang +1 more
TL;DR: New characterizations of the input-to-state stability property are presented and the equivalence between the ISS property and several (apparent) variations proposed in the literature are shown.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Nonlinear Control Systems
Alberto Isidori,M. Thoma,Eduardo D. Sontag,B. W. Dickinson,A. Fettweis,J. L. Massey,J. W. Modestino +6 more
TL;DR: In this paper, a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems is presented, which is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft.
Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
Book
Feedback Systems: Input-output Properties
TL;DR: In this paper, the Bellman-Gronwall Lemma has been applied to the small gain theorem in the context of linear systems and convolutional neural networks, and it has been shown that it can be applied to linear systems.