New Method for the Stability Analysis of Neutral Systems with Time-Varying Structured Uncertainties

2018 ◽  
Author(s):  
Liming Ding ◽  
Dajiang He ◽  
Xianwu Mi ◽  
Jun Shu ◽  
Leiping Chen ◽  
...  
Keyword(s):  
Stability Analysis ◽  
New Method ◽  
Time Varying ◽  
Neutral Systems ◽  
The Stability

scholarly journals Stability Analysis for Neutral and Time-Varying Systems Using Linear Lyapunov Functionals and a Positive Systems Approach

2014 ◽  
Author(s):  
Frédéric Mazenc ◽  
Michael Malisoff
Keyword(s):  
Stability Analysis ◽  
Systems Approach ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Positive Systems ◽  
Neutral Systems ◽  
New Methods ◽  
Higher Dimensional ◽  
Time Varying Systems ◽  
The Stability

We present new methods for proving stability of time-varying linear systems with delays. Our main tools include positive systems and linear Lyapunov functionals. Our work applies to key classes of systems that arise in numerous engineering applications, including neutral systems, and systems that are not necessarily periodic in time and not necessarily positive. We prove stability by comparing the trajectories of the original systems with trajectories of higher dimensional positive systems. One of our key results requires an upper bound on the delay, but the delay can be unknown. Our work also provides robustness of the stability with respect to uncertainties in the coefficient matrices of the system. We illustrate our work in three examples, which show how our methods can sometimes be used with backstepping and linearization to cover even more general classes of systems.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Delayed Trilateral Teleoperation of a Mobile Robot

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
D. Santiago ◽  
E. Slawiñski ◽  
V. Mut
Keyword(s):  
Stability Analysis ◽  
Mobile Robot ◽  
Shared Environment ◽  
Time Varying ◽  
Control Parameters ◽  
Simple Test ◽  
Control Loop ◽  
Teleoperation System ◽  
Human Operators ◽  
The Stability

This paper analyzes the stability of a trilateral teleoperation system of a mobile robot. This type of system is nonlinear, time-varying, and delayed and includes a master-slave kinematic dissimilarity. To close the control loop, three P+d controllers are used under a position master/slave velocity strategy. The stability analysis is based on Lyapunov-Krasovskii theory where a functional is proposed and analyzed to get conditions for the control parameters that assure a stable behavior, keeping the synchronism errors bounded. Finally, the theoretical result is verified in practice by means of a simple test, where two human operators both collaboratively and simultaneously drive a 3D simulator of a mobile robot to achieve an established task on a remote shared environment.

Partial stability analysis of nonlinear time-varying impulsive systems

2019 ◽  
Vol 12 (06) ◽  
pp. 1950066
Author(s):  
Boulbaba Ghanmi
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Time Varying ◽  
Impulsive Systems ◽  
Partial Stability ◽  
Stability Theorems ◽  
Time Varying Systems ◽  
The Stability ◽  
Derivatives Of ◽  
Theoretical Results

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite. With the help of the notion of stable functions, asymptotic partial stability, exponential partial stability, input-to-state partial stability (ISPS) and integral input-to-state partial stability (iISPS) are considered. Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays

2013 ◽  
Vol 341-342 ◽  
pp. 668-673
Author(s):  
Yi Min Li ◽  
Yuan Yuan Li
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Model ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Lmi Optimization ◽  
System A ◽  
The Stability

This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

scholarly journals Stability Analysis of Drilling Inclination System with Time-Varying Delay via Free-Matrix-Based Lyapunov–Krasovskii Functional

2021 ◽  
Vol 25 (6) ◽  
pp. 1031-1038
Author(s):  
Zhen Cai ◽  
Guozhen Hu ◽  
◽  
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay ◽  
Insight Into

This study provides an insight into the asymptotic stability of a drilling inclination system with a time-varying delay. An appropriate Lyapunov–Krasovskii functional (LKF) is essential for the stability analysis of the abovementioned system. In general, an LKF is constructed with each coefficient matrix being positive definite, which results in considerable conservatism. Herein, to relax the conditions of the derived criteria, a novel LKF is proposed by avoiding the positive-definite restriction of some coefficient matrices and introducing additional free matrices simultaneously. Subsequently, this relaxed LKF is applied to derive a less conservative stability criterion for the abovementioned system. Finally, the effect of reducing the conservatism of the proposed LKF is verified based on two examples.

Stability Analysis of a Linearized MEMS

2004 ◽  
Author(s):  
A. Khazaei ◽  
M. Rastgaar Aagaah ◽  
M. Mahinfalah ◽  
N. Mahmoudian ◽  
G. Nakhaie Jazar
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Frequency Response ◽  
Dynamic Behavior ◽  
Stability Theory ◽  
Perturbation Methods ◽  
Time Varying ◽  
Design And Optimization ◽  
System Parameters ◽  
The Stability

This paper presents the stability theory and dynamic behavior of a micro-mechanical parametric-effect resonator. The device is a MEMS time-varying capacitor. The nonlinear dynamics of the MEMS are investigated analytically, and numerically. Applying perturbation methods, and deriving an analytical equation to describe the frequency response of the system enables the designer to study the effect of changes in the system parameters that can be used for design and optimization of the system.

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