scholarly journals Stochastic Bandwidth Packing Process: Stability Conditions via Lyapunov Function Technique

2004 ◽  
Vol 48 (3/4) ◽  
pp. 339-363 ◽  
Author(s):  
David Gamarnik
Keyword(s):  
Lyapunov Function ◽  
Function Technique ◽  
Stability Conditions ◽  
Process Stability ◽  
Packing Process ◽  
Bandwidth Packing

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

scholarly journals Discretized Lyapunov Function Approach for Switched Linear Systems under Dwell Time Constraint

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yongchi Zhao ◽  
Shengxian Zhuang ◽  
Weiming Xiang ◽  
Lin Du
Keyword(s):  
Lyapunov Function ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Time Constraint ◽  
Switched System ◽  
Function Approach ◽  
Disturbance Attenuation ◽  
Function Technique ◽  
Synthesis Process ◽  
Control Synthesis

This paper is concerned with the stability and disturbance attenuation properties of switched linear system with dwell time constraint. A novel time-scheduled Lyapunov function is introduced to deal with the problems studied in this paper. To numerically check the existence of such time-scheduled Lyapunov function, the discretized Lyapunov function technique usually used in time-delay system is developed in the context of switched system in continuous-time cases. Based on discretized Lyapunov function, sufficient conditions ensuring dwell-time constrained switched system global uniformly asymptotically stable are established, then the disturbance attenuation properties in the sense ofL2gain are studied. The main advantage of discretized Lyapunov function approach is that the derived sufficient conditions are convex in subsystem matrices, which makes the analysis results easily used and generalized. Thus, theH∞control synthesis problem is considered. On the basis of analysis results in hand, the control synthesis procedures including both controller and switching law design are unified into one-step method which explicitly facilitates the control synthesis process. Several numerical examples are provided to illustrate the results within our paper.

Stability Predictions for End Milling Operations With a Nonlinear Cutting Force Model

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Alex Elías-Zúñiga ◽  
Jovanny Pacheco-Bolívar ◽  
Francisco Araya ◽  
Alejandro Martínez-López ◽  
Oscar Martínez-Romero ◽  
...  
Keyword(s):  
Experimental Data ◽  
Cutting Force ◽  
End Milling ◽  
Stability Conditions ◽  
Force Model ◽  
Process Stability ◽  
Cutting Force Model ◽  
Stability Lobes ◽  
Milling Operations ◽  
The Stability

The aim of this paper is to obtain the stability lobes for milling operations with a nonlinear cutting force model. The work is focused on the generation of stability lobes based on a formulation with Chebyshev polynomials and the semidiscretization method, considering a nonlinear cutting force model. Comparisons were conducted between experimental data at 5% radial immersion with aluminum workpiece and predictions based on Chebyshev and semidiscretization. In all cases, the use of nonlinear cutting force model provides better prediction of process stability conditions.

On Stability Analysis of Switched Linear Time-Delay Systems under Arbitrary Switching

2015 ◽  
pp. 480-515 ◽  
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Lyapunov Function ◽  
Continuous Time ◽  
Delay System ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Arbitrary Switching ◽  
The Stability

This chapter focuses on the stability analysis problem for a class of continuous-time switched time-delay systems modelled by delay differential equations under arbitrary switching. Then, a transformation under the arrow form is employed. Indeed, by using a constructed Lyapunov function, the aggregation techniques, the Kotelyanski lemma associated with the M-matrix properties, new delay-dependent sufficient stability conditions are derived. The obtained results provide a solution to one of the basic problems in continuous-time switched time-delay systems. This problem ensures asymptotic stability of the switched time-delay system under arbitrary switching signals. In addition, these stability conditions are extended to be generalized for switched systems with multiple delays. Noted that, these obtained results are explicit, simple to use, and allow us to avoid the problem of searching a common Lyapunov function. Finally, two examples are provided, with numerical simulations, to demonstrate the effectiveness of the proposed method.

Tracking Control for a Class of Switched Fuzzy Systems

2014 ◽  
Vol 635-637 ◽  
pp. 1378-1381 ◽  
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Lyapunov Function ◽  
Tracking Control ◽  
Design Problem ◽  
Fuzzy Systems ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Function Technique ◽  
Control Law ◽  
State Dependent ◽  
Switching Method

This paper investigates the problems of tracking control for switched fuzzy systems. Based on the state-dependent switching method, sufficient conditions for the solvability of the tracking control problem are given. We use single Lyapunov function technique to design a tracking control law. The controller design problem can be solved efficiently. A numerical example is given to show the effectiveness of our method.

SOS Stability Conditions for Nonlinear Systems Based on a Polynomial Fuzzy Lyapunov Function

2011 ◽  
Vol 44 (1) ◽  
pp. 12777-12782 ◽  
Author(s):  
Kevin Guelton ◽  
Noureddine Manamanni ◽  
Darius L. Koumba-Emianiwe ◽  
Cuong Duong Chinh
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Stability Conditions ◽  
Fuzzy Lyapunov Function

Absolute Stability of a Class of Singular Nonlinear Systems with Set-Valued Mappings

2014 ◽  
Vol 24 (01) ◽  
pp. 1550015 ◽  
Author(s):  
Gaoming Feng ◽  
Xingguo Tan
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Absolute Stability ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Set Valued Mappings ◽  
The Absolute

A class of singular nonlinear systems with set-valued mappings are studied in this paper. Criteria are given based on the Lyapunov function to check the absolute stability of the systems, then the results are extended to the time delay systems and the time delay systems with uncertainty. Three examples are simulated to show the effectiveness of the proposed stability conditions.

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