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.

scholarly journals Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. Nosov ◽  
J. A. Meda-Campaña ◽  
J. C. Gomez-Mancilla ◽  
J. O. Escobedo-Alva ◽  
R. G. Hernández-García
Keyword(s):  
Stability Analysis ◽  
Finite Number ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Switched System ◽  
Linear Functions ◽  
Asymptotically Stable ◽  
Multiple Lyapunov Functions ◽  
Stability Theorems ◽  
The Stability

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

Lyapunov-Based Sufficient Conditions for Nonlinear Impulsive Systems

2011 ◽  
Vol 219-220 ◽  
pp. 508-512
Author(s):  
Yong Liang Gao ◽  
Xiao Wu Mu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Invariant Set ◽  
Positive Definite ◽  
Impulsive Systems ◽  
Stability Theorems ◽  
Sufficient Conditions For Convergence ◽  
The Stability

This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. A set of Lyapunov-based sufficient conditions are established for these convergent properties. These results do not require the Lyapunov function to be positive definite. Inequalities relating the righthandside of the differential equation and the Lyapunov function derivative are involved for these results. These inequalities make it possible to deduce properties of the functions and thus leads to sufficient conditions for convergence and 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.

The Corduneanu-Popov Approach to the Stability of Nonlinear Time-Varying Systems

1970 ◽  
Vol 18 (2) ◽  
pp. 267-281 ◽  
Author(s):  
James H. Taylor ◽  
Kumpati S. Narendra
Keyword(s):  
Time Varying ◽  
Time Varying Systems ◽  
The Stability
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