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On stability of switched homogeneous nonlinear systems

Lijun Zhang, Sheng Liu, Hai Lan
2007 Journal of Mathematical Analysis and Applications  
In this paper, the problem of stability of switched homogeneous systems is addressed.  ...  Then for planar switched homogeneous systems, an LMI approach to stability of planar switched homogeneous systems is presented.  ...  Based on this result, stability of switched homogeneous systems was studied.  ... 
doi:10.1016/j.jmaa.2006.12.065 fatcat:gnwcutdkonam7cbl5zrqkix6om

Stability of Discrete-Time Switched Homogeneous Systems on Cones and Conewise Homogeneous Inclusions

Jinglai Shen, Jianghai Hu
2012 SIAM Journal of Control and Optimization  
This paper presents a stability analysis of switched homogenous systems on cones under arbitrary and optimal switching rules with extensions to conewise homogeneous or linear inclusions.  ...  At x e = 0, the SHS (1) on C is called • locally strongly stable if for any ε > 0, a neighborhood N of x e in C exists such that for any z ∈ N , x(t; z, σ) < ε, ∀ t ∈ Z + , under any switching sequence  ...  The focus is on switched homogeneous systems (SHSs) on cones.  ... 
doi:10.1137/110845215 fatcat:3tde5u2jk5hyhh4h4qffgdseoe

Sum of Squares Certificates for Stability of Planar, Homogeneous, and Switched Systems

Amir Ali Ahmadi, Pablo A. Parrilo
2017 IEEE Transactions on Automatic Control  
This result is extended to show that such sos-based certificates of stability are guaranteed to exist for all stable switched linear systems.  ...  Finally, we demonstrate some merits of replacing the sos requirement on a polynomial Lyapunov function with an sos requirement on its top homogeneous component.  ...  SOS certificates for stability of switched linear systems The result of Theorem 3.3 extends in a straightforward manner to Lyapunov analysis of switched systems.  ... 
doi:10.1109/tac.2016.2647253 fatcat:5xepmhivw5dw7caffz7bmqy4rm

On Finite-Time Stability of Switched Systems with Hybrid Homogeneous Degrees

Bin Zhang
2018 Mathematical Problems in Engineering  
The finite-time stability is investigated for switched nonlinear systems. It is assumed that each subsystem possesses a positive homogeneous Lyapunov-like function.  ...  The derivative of the function is with hybrid homogenous degrees. Three substantially different situations are considered and different sufficient conditions are provided, respectively.  ...  Acknowledgments This work was supported by the National Natural Science Foundation of China (61603050) and the Fundamental Research Funds for the Central Universities (2017RC25).  ... 
doi:10.1155/2018/3096986 fatcat:jwntadx6engc5mnu7ttzv6psia

Comments on "On stability of switched homogeneous nonlinear systems" by Lijun Zhang, Sheng Liu, and Hai Lan [J. Math. Anal. Appl. 334 (1) (2007) 414–430]

Alexander O. Ignatyev
2011 Journal of Mathematical Analysis and Applications  
In the above paper [1], a sufficient condition is obtained for stability of switched nonlinear homogeneous systems. The obtained results are essentially based on the following lemma and remark.  ...  We show that the proof of the results obtained in the above paper is wrong since it is based on lemma which is not true. Therefore the results of the paper cannot be considered as true ones.  ...  According to Lemma 1, the existence of the quadratic Lyapunov function is a sufficient and necessary condition for stable homogeneous systems.  ... 
doi:10.1016/j.jmaa.2010.05.046 fatcat:r3zz2qmarnak7pl7xexv3j6hy4

Homogeneous Stabilizer by State Feedback for Switched Nonlinear Systems Using Multiple Lyapunov Functions' Approach

Hui Ye, Bin Jiang, Hao Yang
2017 Mathematical Problems in Engineering  
This paper investigates the problem of global stabilization for a class of switched nonlinear systems using multiple Lyapunov functions (MLFs).  ...  Based on adding a power integrator technique, we design homogeneous state feedback controllers of all subsystems and a switching law to guarantee that the closed-loop system is globally asymptotically  ...  Conflicts of Interest The authors declare that they have no conflicts of interest.  ... 
doi:10.1155/2017/5034316 fatcat:xg5ow5gxjbeotniqjwe2stmnkq

Stabilization of a Class of Switched Positive Nonlinear Systems

Xing Xing, Zhichun Jia, Yunfei Yin, Tingting Wu
2015 Mathematical Problems in Engineering  
The problem of switching stabilization for a class of switched positive nonlinear systems (switched positive homogeneous cooperative system (SPHCS) in the continuous-time context and switched positive  ...  A sufficient condition of stabilization for SPHCSs with unstable positive subsystems is derived in continuous-time context.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2015/152410 fatcat:jlobiqvrgjdyfei54agntlowzq

Exponential Stability of Switched Positive Homogeneous Systems

Dadong Tian, Shutang Liu
2017 Complexity  
This paper studies the exponential stability of switched positive nonlinear systems defined by cooperative and homogeneous vector fields.  ...  Then, we present a sufficient condition of exponential stability under minimum dwell time switching for the switched positive nonlinear systems. Some results in the previous literature are extended.  ...  Acknowledgments This work was supported by the Key Program of National Natural Science Foundation of China (no. 61533011) and the National Natural Science Foundation of China (no. 61473133).  ... 
doi:10.1155/2017/4326028 fatcat:kikxal2vajagpdrt5254lwhgi4

Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems [article]

Matthew Abate, Corbin Klett, Samuel Coogan, Eric Feron
2020 arXiv   pre-print
This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems.  ...  This creates an intuitive procedure for checking the stability properties of switched linear systems and a computationally competitive algorithm is presented for generating high-order homogeneous polynomial  ...  STABILITY AND SWITCHED LINEAR SYSTEMS A.  ... 
arXiv:1906.04810v3 fatcat:ixznfb44wzdsjm3iy4wqqviy6m

Switched Convergence of Second-Order Switched Homogeneous Systems

Carmen Pérez, Francisco Benítez
2013 Abstract and Applied Analysis  
This paper studies the stabilization of second-order switched homogeneous systems.  ...  We present results that solve the problem of stabilizing a switched homogeneous system; that is, we establish necessary and sufficient conditions under which the stabilization is assured.  ...  However, for switched homogeneous systems, the problem of stabilization, that is, the problem of constructing a switching law that stabilizes the system, is still open.  ... 
doi:10.1155/2013/472430 fatcat:2u7duzykyjez7ou4jtcizc62by

Optimal Control of Switched Homogeneous Systems

Michael Rinehart, Munther Dahleh, Ilya Kolmanovsky
2007 American Control Conference (ACC)  
In this paper, we present a method for designing discrete-time state-feedback controllers for a class of continuous-time switched homogeneous systems which includes switched linear systems as a special  ...  To illustrate the results, the methodology is applied to an example switched system possessing two unstable modes, one of which is nonlinear.  ...  Davor Hrovat for his initiation of this joint project. This research is sponsored by Ford Research and Advanced Engineering, Ford Motor Company.  ... 
doi:10.1109/acc.2007.4282382 dblp:conf/acc/RinehartDK07 fatcat:rxe5g5iq4fd7lize5jiekvrg3i

Stability Analysis of Nonlinear Switched Systems via Reduction Method

Stanislav N. Vassilyev, Alexander A. Kosov, Alexander I. Malikov
2011 IFAC Proceedings Volumes  
Stability of nonlinear switched systems is discussed.  ...  A method of constructing the common (scalar and vector) Lyapunov functions is proposed for switched systems whose equations have homogenous right-hand sides and for switched large-scale systems containing  ...  In the present paper, we consider also the issue of stability of large-scale systems with switched homogeneous subsystems and switched interconnections (Section 4).  ... 
doi:10.3182/20110828-6-it-1002.01936 fatcat:lw4nsdlw2ve4pibih4wrqrpkz4

Page 6678 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
We propose a dwell-time function which depends on the comparison functions which characterize the in- tegral input-to-state stability property and guarantees the state of the switched system to converge  ...  Summary: “The asymptotic convergence of a switched nonlin- ear system in the presence of disturbances is studied. The system switches among a family of integral input-to-state stable systems.  ... 

State-feedback stabilizability in switched homogeneous systems

Federico Najson
2009 2009 American Control Conference  
The present article is concerned with statefeedback stabilizability of discrete-time switched homogeneous systems.  ...  Equivalently, a switched homogeneous system is statefeedback exponentially stabilizable if and only if an associated dynamic programming equation admits a solution on a given convex set.  ...  In [4] , three basic problems concerning the stability of switched systems are recognized: (1) The problem of finding conditions for stability, for arbitrary switching signals.  ... 
doi:10.1109/acc.2009.5159973 dblp:conf/amcc/Najson09 fatcat:jsxfaomcmva7pfrpznkztu2wga

Stability Analysis of Second-Order Switched Homogeneous Systems

David Holcman, Michael Margaliot
2002 SIAM Journal of Control and Optimization  
We study the stability of second-order switched homogeneous systems.  ...  Using the duality between stability analysis and control synthesis, this also leads to a novel algorithm for designing a stabilizing switching controller.  ...  We presented a new approach to stability analysis of second-order switched homogeneous systems based on the idea of generalized first integrals.  ... 
doi:10.1137/s0363012901389354 fatcat:r5bdabvwjvhdjgabcrvhmohsgu
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