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Page 6354 of Mathematical Reviews Vol. , Issue 91K
[page]
1991
Mathematical Reviews
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The concept of Lyapunov stability for normal (explicit) first-order, continuous-time, nonlinear differential systems x(t) = f(t, x(t)), x,f € R", is extended to general implicit differential systems f( ...
(YU-BORIS)
Nonlinear functions and stability of motions of implicit differential systems.
Internat. J. Control 52 (1990), no. 5, 1167-1187. ...
Towards scalable algorithms with formal guarantees for Lyapunov analysis of control systems via algebraic optimization
2014
53rd IEEE Conference on Decision and Control
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, and controller synthesis can be addressed by a synergy of classical tools from Lyapunov theory and modern computational techniques from algebraic optimization. ...
Exciting recent developments at the interface of optimization and control have shown that several fundamental problems in dynamics and control, such as stability, collision avoidance, robust performance ...
Even for the class of polynomial differential equations of degree two, we do not currently know whether there is a finite time (let alone polynomial time) algorithm that can decide stability. ...
doi:10.1109/cdc.2014.7039734
dblp:conf/cdc/AhmadiP14
fatcat:kaahigfyavfsta47vwldaiht64
Page 5819 of Mathematical Reviews Vol. , Issue 93j
[page]
1993
Mathematical Reviews
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The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. ...
(I-NAPL-I)
Stability robustness of interval matrices via Lyapunov quadratic forms. (English summary)
IEEE Trans. Automat. Control 38 (1993), no. 2, 281-284. ...
Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems
2008
2008 47th IEEE Conference on Decision and Control
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Here, connections to the method of piecewise quadratic Lyapunov functions are made. Finally, we examine systems with arbitrary switching between a finite set of matrices. ...
We relax the monotonicity requirement of Lyapunov's theorem to enlarge the class of functions that can provide certificates of stability. ...
In [6] , the method of piecewise quadratic (PWQ) Lyapunov functions was introduced to analyze stability of continuous time PWA systems. ...
doi:10.1109/cdc.2008.4739402
dblp:conf/cdc/AhmadiP08
fatcat:nzhee7gm6jahndk37nk6wt66ly
Page 2722 of Mathematical Reviews Vol. , Issue 97D
[page]
1997
Mathematical Reviews
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Relations of the problem with two robust stability analysis problems: the Hurwitz stability of families of polynomi- als and the quadratic stability of uncertain time-varying linear systems, are discussed ...
An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.”
97d:93062 93D05 34D10 Nurges, Ulo (ES-AOS-A; Tallinn) On the Schur stability ...
Page 9480 of Mathematical Reviews Vol. , Issue 2004k
[page]
2004
Mathematical Reviews
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A share the common quadratic Lyapunov function x’ Mx for all A €¢ A. ...
Vii Ngoc Phat (VN-HMI; Hanoi)
2004k:93102 93D15 34D20 93D05 Cheng, Daizhan (PRC-ASBJ-S; Beijing) Stabilization via polynomial Lyapunoy function. ...
Stability Domains for Quadratic-Bilinear Reduced-Order Models
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2009.02769v1 fatcat:vutucoseunfspl3wbdzv2lje6y
In this work, for a given quadratic Lyapunov function, we first derive an analytical estimate of the stability domain, which is rather conservative but can be evaluated efficiently. ...
We propose a computational approach to estimate the stability domain of quadratic-bilinear reduced-order models (ROMs), which are low-dimensional approximations of large-scale dynamical systems. ...
In [20] , an analytical method for estimating the domain of attraction of polynomial systems is proposed via parametrized quadratic Lyapunov functions. ...
arXiv:2009.02769v2
fatcat:uvt5t7gx6jebrdekzwu7cau6o4
Page 1220 of Mathematical Reviews Vol. , Issue 95b
[page]
1995
Mathematical Reviews
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Much of the literature on robust linear systems in state space formulation has concentrated on common (quadratic) Lyapunov functions for a given set of uncertainties. ...
O. (5-ANU-SE; Canberra);
Fu, Minyue (5-NEWC-E; Newcastle)
Lyapunov functions for uncertain systems with applications to the stability of time varying systems. (English summary)
IEEE Trans. ...
Page 5917 of Mathematical Reviews Vol. , Issue 86m
[page]
1986
Mathematical Reviews
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Michel, Anthony N. (1-NDM-E); Miller, Richard K. (1-IASU)
Stability analysis of discrete-time interconnected
systems via computer-generated Lyapunov functions
with applications to digital filters. ...
The general results are used for obtaining sufficient conditions for technical stability on a finite interval of time of a nonlinear process of propagation of electromagnetic vibrations along a cable.” ...
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
2009
IEEE Transactions on Automatic Control
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After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization ...
During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. ...
Common Quadratic Lyapunov Functions The existence of a common quadratic Lyapunov function (CQLF) for all its subsystems assures the quadratic stability of the switched system. ...
doi:10.1109/tac.2008.2012009
fatcat:k5aa5khwszbb7in5jax35lv6ry
Page 3958 of Mathematical Reviews Vol. , Issue 2003e
[page]
2003
Mathematical Reviews
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A robust state feedback control law based on it is constructed via the sequential quadratic programming method to stabilize uncertain systems. ...
Systems Sci. 33 (2002), no. 2, 81-86.
A feedback stabilization law is derived for linear time-delay systems in the presence of norm-bounded nonlinear uncertainties. ...
Page 1651 of Mathematical Reviews Vol. , Issue 87c
[page]
1987
Mathematical Reviews
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The authors also briefly discuss time-delayed systems, prob- lems of technical stability and problems of local optimal control synthesis of dynamic systems via the Lyapunov method. ...
Studies in the stability of systems with distributed parameters by the Lyapunov function method. (Russian) Stability of motion, 3-22, 249, ‘‘Nauka’”’ Sibirsk. Otdel., Novosibirsk, 1985. ...
Lower bounds on complexity of Lyapunov functions for switched linear systems
2016
Nonlinear Analysis. Hybrid Systems
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a polynomial Lyapunov function of degree ≤ d, or (ii) a polytopic Lyapunov function with ≤ d facets, or (iii) a piecewise quadratic Lyapunov function with ≤ d pieces. ...
Index terms: stability of switched systems, linear difference inclusions, the finiteness conjecture of the joint spectral radius, convex optimization for Lyapunov analysis. ...
We shall also remark that for continuous time switched linear systems, [30] have established that the degree of a polynomial Lyapunov function for an ASS system may be arbitrarily high, answering a question ...
doi:10.1016/j.nahs.2016.01.003
fatcat:pxqq6jc7bjgb7inimnp5m2rwbu
New Lyapunov function and extra information on membership functions for improving stability conditions of TS systems
2011
IFAC Proceedings Volumes
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To derive LMI based stability condition using the proposed new fuzzy Lyapunov function two ideas are invoked: i) the inclusion of the membership function time-derivative information using a finite number ...
This paper presents an improved stability condition for Takagi-Sugeno (TS) fuzzy systems based on a new fuzzy Lyapunov function. ...
In the context of TS systems this function is parametrized by a polynomial combination of the membership functions. ...
doi:10.3182/20110828-6-it-1002.01924
fatcat:nlzeovksijcwvk5iq2f564b4lu
2007 Index IEEE Transactions on Automatic Control Vol. 52
2007
IEEE Transactions on Automatic Control
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., H Control and Estimation of Retarded State-Multiplicative Stochastic Systems; TAC Sept. 1773Sept. ...
J., Approximation Metrics for Discrete and Continuous Systems; TAC May 2007 782-798 Giua, A., see Basile, F., TAC Feb. 2007 306-311 Giua, A., Seatzu, C., and Corona, C., Oct. 2007 Oct. ...
H Filtering of Discrete-Time Switched Systems With State Delays via Switched Lyapunov Function Approach. ...
doi:10.1109/tac.2007.913948
fatcat:vpztpth7jnhk7b5o5bt2nyrrdm
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