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A new class of Lyapunov functions for nonstandard switching systems: The stability analysis problem

Carlos A. Cavichioli Gonzaga, Marc Jungers, Jamal Daafouz, Eugenio B. Castelan
2011 IEEE Conference on Decision and Control and European Control Conference  
This paper presents a new class of Lur'e type Lyapunov functions for a discrete-time switched system interconnected with a switched nonlinearity satisfying a modedependent cone bounded condition.  ...  systems and local stability analysis for these systems with an additional saturating input consisting of a switched linear state feedback.  ...  Based on this new Lyapunov function, we tackle two different stability analysis problems of switching systems.  ... 
doi:10.1109/cdc.2011.6161130 dblp:conf/cdc/GonzagaJDC11 fatcat:2z4ysmmygrfsreszjxrp4zakwy

Local robust regulation of chained systems

E. Valtolina, A. Astolfi
2003 Systems & control letters (Print)  
In this work a discontinuous control law for (nonholonomic) chained systems yielding global asymptotic (exponential) regulation and local robustness against the e ect of (small) external disturbances is  ...  Acknowledgements The authors are grateful to the anonymous reviewers for the constructive comments. The work of E. Voltolina and A. Astolÿ is partially supported by the TMR Network NACO2.  ...  It must be noted that, because of lack of regularity, the function V ( x) 7 A similar analysis applies if x 1 ¡ 0. 8 As z(x(0)) = k + ¡ + ∞, x 1 (0) = 0. is not a Lyapunov function, hence it is not  ... 
doi:10.1016/s0167-6911(02)00327-4 fatcat:rk4e5rzlcfcd7afxeewdlwyvem

Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

R.T. M'Closkey, R.M. Murray
1997 IEEE Transactions on Automatic Control  
The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra.  ...  This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback.  ...  ACKNOWLEDGMENT The authors would like to thank L. Praly and the reviewers for their thoughtful comments.  ... 
doi:10.1109/9.580865 fatcat:zwmzfezbhzddflsmkptqnvbmqy

Fuzzy Synchronization Control for Fractional-Order Chaotic Systems With Different Structures

Jin Xu, Ning Li, Xiulan Zhang, Xiaoli Qin
2020 Frontiers in Physics  
This paper discusses the synchronization problem for a class of unknown fractional-order chaotic systems (FOCSs) with indeterminate external disturbances and non-symmetrical control gain.  ...  A paralleled adaptive fuzzy synchronization controller is constructed in which indeterminate non-linear functions are approximated by the fuzzy logic systems depending on fractional-order Lyapunov stability  ...  Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems.  ... 
doi:10.3389/fphy.2020.00155 doaj:9ab9a6050d7b4db39131c925e29e5edf fatcat:al3s2lxcezej3fe6qmpcqql2zq

Node weighted scheduling

Gagan R. Gupta, Sujay Sanghavi, Ness B. Shroff
2009 Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems - SIGMETRICS '09  
This paper proposes a new class of online policies for scheduling in input-buffered crossbar switches.  ...  Most algorithms for switch scheduling take an edge based approach; in contrast, we focus on scheduling (a large enough set of) the most congested ports.  ...  Our Lyapunov function is evocative of the one used by [6] for the analysis of Greedy (GMM).  ... 
doi:10.1145/1555349.1555361 dblp:conf/sigmetrics/GuptaSS09 fatcat:3wpiu5bv3vcu5hwllnku5re4z4

Passivity and stability of switched systems under quantization

Feng Zhu, Han Yu, Michael J. McCourt, Panos J. Antsaklis
2012 Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control - HSCC '12  
Passivity theory is a well-established tool for analysis and synthesis of dynamical systems.  ...  The contribution in this paper is to introduce a control framework under which passivity for switched and non-switched systems can be maintained.  ...  ACKNOWLEDGMENTS The support of the National Science Foundation under Grant No. CNS-1035655 is gratefully acknowledged.  ... 
doi:10.1145/2185632.2185668 dblp:conf/hybrid/ZhuYMA12 fatcat:bw3toj2nqve6df7klyykm76tva

Frameworks in Problems of Structural Identification Systems

Nikolay Karabutov
2017 International Journal of Intelligent Systems and Applications  
Algorith ms for an estimat ion of a nonlinearity class on the basis of the analysis of sector sets are proposed.  ...  The possibility of application VF for the problem solving of identification static systems is shown.  ...  Therefore, Lyapunov exponents (LE) often apply to the analysis of reasons for its cause. LE is one of the structural performances, allowing tracing a system evolution.  ... 
doi:10.5815/ijisa.2017.01.01 fatcat:kvjciifbpjh4vcjpso3cbvwwrq

Robust Stability of Networks of iISS Systems: Construction of Sum-Type Lyapunov Functions

Hiroshi Ito, Zhong-Ping Jiang, Sergey N. Dashkovskiy, Bjorn S. Ruffer
2013 IEEE Transactions on Automatic Control  
To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of a sum of nonlinearly rescaled  ...  This paper gives a solution to the problem of verifying stability of networks consisting of integral input-tostate stable (iISS) subsystems.  ...  The stability analysis of general iISS networks is formulated and recast as a problem of constructing a sum-type Lyapunov function in Section III. A solution is presented in Section IV.  ... 
doi:10.1109/tac.2012.2231552 fatcat:e3ovlj2f4zboxmhnpo2xkieyca

Nonstandard Hopf bifurcation in switched [article]

Xiao-Song Yang, Songmei Huan
2010 arXiv   pre-print
This paper presents an analysis on nonstandard generalized Hopf bifurcation in a class of switched systems where the lost of stability of linearized systems is not due to the crossing of their complex  ...  conjugate eigenvalues but relevant to the switching laws between the subslystems.  ...  Acknowledgements This work is supported in part by National Natural Science Foundation of China (10972082).  ... 
arXiv:1001.2068v1 fatcat:o4g2hikiczh6bkmnj53dt2426e

Real-Time Reachability for Verified Simplex Design

Stanley Bak, Taylor T. Johnson, Marco Caccamo, Lui Sha
2014 2014 IEEE Real-Time Systems Symposium  
The problem of precisely and correctly defining this switching logic has previously been considered either using a controltheoretic optimization approach, or through an offline hybrid systems reachability  ...  The Simplex Architecture ensures the safe use of an unverifiable complex controller by using a verified safety controller and verified switching logic.  ...  the Lyapunov function from the LMI method is only a sufficient condition for safe switching).  ... 
doi:10.1109/rtss.2014.21 dblp:conf/rtss/BakJCS14 fatcat:dvoeivikknhm3bpeaq6xpwwqfy

Real-Time Reachability for Verified Simplex Design

Taylor T. Johnson, Stanley Bak, Marco Caccamo, Lui Sha
2016 ACM Transactions on Embedded Computing Systems  
The problem of precisely and correctly defining this switching logic has previously been considered either using a controltheoretic optimization approach, or through an offline hybrid systems reachability  ...  The Simplex Architecture ensures the safe use of an unverifiable complex controller by using a verified safety controller and verified switching logic.  ...  the Lyapunov function from the LMI method is only a sufficient condition for safe switching).  ... 
doi:10.1145/2723871 fatcat:aomr5vi5hnh25bd5633l26zwkq

Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model [article]

Manh Tuan Hoang
2021 arXiv   pre-print
The aim of this work is to study qualitative dynamical properties of a generalized hepatitis B epidemic model and its dynamically consistent discrete model.  ...  Lyapunov, The general problem of the stability of motion, International Journal of Control, Taylor & Francis, 1992. [43] K. Manna, S. P.  ...  Kojouharov, A class of nonstandard numerical methods for autonomous dynamical systems, Applied Mathematics Letters 50(2015) 78-82. [63] D. T. Wood, H. V. Kojouharov, D. T.  ... 
arXiv:2112.06284v1 fatcat:5gi5zdmkenesnk42ybwcxq6tsm

Neural network-based flight control systems: Present and future

Seyyed Ali Emami, Paolo Castaldi, Afshin Banazadeh
2022 Annual Reviews in Control  
To this end, in this paper, we will provide a detailed mathematical view of Neural Network (NN)-based flight control systems and the challenging problems that still remain.  ...  Various supplementary features, which can be integrated with a basic IFCS such as the fault-tolerance capability, the consideration of system constraints, and the combination of NNs with other robust and  ...  The practical finite-time stability of the closed-loop system has been proved using a simple Lyapunov function as V = 1/2s 2 assuming that a PD controller can stabilize the system [48] .  ... 
doi:10.1016/j.arcontrol.2022.04.006 fatcat:ja4juxuxp5aodjjcodjjfppz7e

Bifurcations in two-dimensional piecewise smooth maps-theory and applications in switching circuits

S. Banerjee, P. Ranjan, C. Grebogi
2000 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a fixed point crosses the border between the smooth regions in the state  ...  In this paper we present a systematic analysis of such bifurcations through a normal form: the piecewise linear approximation in the neighborhood of the border.  ...  ACKNOWLEDGMENT The authors would like to thank Prof. J. A. Yorke and Dr. G. H. Yuan of the University of Maryland, College Park, for discussions, especially in the initial stages of this work.  ... 
doi:10.1109/81.847870 fatcat:ncbvvpmq2nex3cprz6mem4xcaq

Pattern generation and the control of nonlinear systems

R.W. Brockett
2003 IEEE Transactions on Automatic Control  
In this paper, we develop a linkage between the use of cyclic processes and the control of nonholonomic systems, emphasizing the problem of achieving stable regulation.  ...  The discussion brings to the fore characteristic phenomena that distinguish the regulation problem for such strongly nonlinear systems from the more commonly studied linear feedback regulators.  ...  We define stabilizing control laws for large classes of systems, drawing a distinction between the cases where regulation involves both frequency and amplitude adjustment and the case where amplitude adjustment  ... 
doi:10.1109/tac.2003.817927 fatcat:qa2ft7rgi5finaisqv27ufyn6m
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