Feedback Stabilization of Nonlinear Systems: Sufficient Conditions and Lyapunov and Input-output Techniques

1995 ◽  
pp. 293-348 ◽  
Author(s):  
Jean-Michel Coron ◽  
Laurent Praly ◽  
Andrew Teel
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Input Output

scholarly journals L1 Input-Output Finite-Time Control of Positive Switched Nonlinear Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Leipo Liu ◽  
Xiangyang Cao ◽  
Bo Fan ◽  
Zhumu Fu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Distributed Delays ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Input Output ◽  
Positive Type ◽  
Time Control

In this paper, the problem of L1 input-output finite-time control of positive switched nonlinear systems with time-varying and distributed delays is investigated. Nonlinear functions considered in this paper are located in a sector field. Firstly, the proof of the positivity of switched positive nonlinear systems with time-varying and distributed delays is given, and the concept of L1 input-output finite-time stability (L1 IO-FTS) is firstly introduced. Then, by constructing multiple co-positive-type nonlinear Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are derived to guarantee the corresponding closed-loop system is L1 IO-FTS. Such conditions can be easily solved by linear programming. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Identifiability of Nonlinear Systems With Hysteretic Elements

1983 ◽  
Vol 105 (4) ◽  
pp. 209-214 ◽  
Author(s):  
A. M. Andronikou ◽  
G. A. Bekey ◽  
F. Y. Hadaegh
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Input Output ◽  
Hysteretic System ◽  
Deterministic Systems ◽  
Equivalent Systems

This paper is concerned with the conditions under which deterministic systems containing a hysteresis-type nonlinearity are identifiable from input-output measurements. The approach to the problem requires that identifiability conditions for appropriately defined nearly-equivalent systems be obtained initially. Then conditions under which identifiability of the nearly-equivalent nonlinear (but non-hysteretic) system imply the identifiability of the original hysteretic system are obtained. Sufficient conditions for identifiability of these systems are presented.

scholarly journals Disturbance Observer-Based Input-Output Finite-Time Control of a Class of Nonlinear Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Leipo Liu ◽  
Xiaona Song ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Disturbance Observer ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Law ◽  
Input Output ◽  
Classical State ◽  
Time Control

This paper is concerned with disturbance observer-based input-output finite-time control of a class of nonlinear systems with one-sided Lipschitz condition, as well as multiple disturbances. Firstly, a disturbance observer is constructed to estimate the disturbance generated by an exogenous system. Secondly, by integrating the estimation of disturbance with a classical state feedback control law, a composite control law is designed and sufficient conditions for input-output finite-time stability (IO-FTS) of the closed-loop system are attained. Such conditions can be converted into linear matrix inequalities (LMIs). Finally, two examples are given to show the effectiveness of the proposed method.

Proportional Nonlinear Systems: A Liable Class for Global Exponential State-Feedback Stabilization

2013 ◽  
Author(s):  
Francesco Carravetta
Keyword(s):  
Nonlinear Systems ◽  
Algebraic System ◽  
State Feedback ◽  
Original System ◽  
Two Dimensions ◽  
Feedback Stabilization ◽  
Medial Part ◽  
Input Output ◽  
Proportional Systems ◽  
Output Behavior

We introduce, through an analysis overall restricted, for the sake of simplicity, in two-dimensions, the class of proportional systems, a nice subclass of the ΣΠ-algebraic nonlinear systems that we formerly introduced in another paper as a sort of ‘non-linear paradigm’ linking nonlinear to bilinear systems. Also we define a decomposition, which every ΣΠ-algebraic system undergoes, into the cascade of a driver, medial and final bilinear subsystem, having the same input-output behavior as the original. We show that a systematic way for global feedback stabilization can be developed for the class of proportional systems, leading to the global feedback exponential stabilization of the medial part under some ‘natural’ condition of non singularity. We show in an example the capability of the proposed method to achieving global feedback stabilization for the original system as well.

scholarly journals Quantized State Feedback Stabilization of Nonlinear Systems under Denial-of-Service

2021 ◽  
Vol 54 (9) ◽  
pp. 323-328
Author(s):  
Ming Shi ◽  
Shuai Feng ◽  
Hideaki Ishii
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Denial Of Service ◽  
Feedback Stabilization
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