A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On Existence of Solutions to Structured Lyapunov Inequalities
[article]

2016
*
arXiv
*
pre-print

In this paper, we derive sufficient conditions

arXiv:1603.07686v1
fatcat:qvzdpt4azvcyrpe6n4ozprca54
*on*drift matrices under which block-diagonal*solutions**to**Lyapunov**inequalities**exist*. ... We finally show how*to*construct these*solutions*in some cases without solving the full*Lyapunov**inequality*. ... Hence, major questions still remain concerning*existence*theorems and scalable computation*of*block-diagonal*solutions**to**Lyapunov**inequalities*. ...##
###
Page 507 of American Society of Civil Engineers. Collected Journals Vol. 123, Issue ST4
[page]

1997
*
American Society of Civil Engineers. Collected Journals
*

If tmin < 0, there

*exists*a*solution**of*the*Lyapunov**inequalities*, whereas t,i, = O means that the*solution*does not*exist*. ... Note that*Lyapunov*matrix*inequalities*, (14), are linear matrix*inequalities*. Khalil (1992) has presented the con- ditions for the*existence**of*the*solution**of*simultaneous Lya- punov*inequalities*. ...##
###
Forwarding Design With Prescribed Local Behavior

2013
*
IEEE Transactions on Automatic Control
*

Among the non-linear control techniques, some

doi:10.1109/tac.2013.2277632
fatcat:5n5zyotfqffzre5oc6vojrvt7u
*Lyapunov*design methods (Forwarding/Backstepping) take advantage*of*the*structure**of*the system (Feedforward-form/Feedback-form)*to*formulate a continuous ... In addition*to*stabilization, we focus*on*the local behaviour*of*the closed loop system, providing conditions under which we can predetermine the behaviour around the origin for Feedforward systems. ... Indeed, this*one*is*of*rank . In order*to*apply Theorem 1, we need*to*find*solution**to*the weak*Lyapunov**inequality*(10) and (5) . ...##
###
A necessary and sufficient minimality condition for uncertain systems

1999
*
IEEE Transactions on Automatic Control
*

This condition is based

doi:10.1109/9.793720
fatcat:ylyxgokov5h2ri7jnbclumveiq
*on*the*existence**of*a rank-deficient*solution**to*either*of*a pair*of*linear matrix*inequalities*which generalize*Lyapunov*equations; the notion*of*Gramians is thus also generalized ... Subsequent results, such as the definition*of*and rank tests*on**structured*controllability and observability matrices are also given. ... all operators in a neighborhood*of*zero if and only if there*exist*singular*structured**solutions**to*the*Lyapunov**inequalities*. ...##
###
Nonlinear Stabilization via Control Lyapunov Measure

2010
*
IEEE Transactions on Automatic Control
*

Using this approach, the codesign problem leads

doi:10.1109/tac.2010.2042226
fatcat:pd7nu7zovffyzctsymynujgbry
*to*a finite number*of*linear*inequalities*whose*solutions*define the feasible set*of*stabilizing controllers. ... We provide a proof*of**existence*for a stochastic version*of*such a controller while the deterministic restriction is posed as the*solution**of*a related integer programming problem. ...*Existence**of*a Stochastic Controller The*existence**of*a stochastic controller is linked*to*whether a*solution**exists**to*the set*of**inequalities*given by ∑ i,a R ia P a i j < α ∑ a R ja , j = 1, . . . , ...##
###
Nonlinear stabilization via control-Lyapunov measure

2007
*
2007 46th IEEE Conference on Decision and Control
*

Using this approach, the codesign problem leads

doi:10.1109/cdc.2007.4434956
dblp:conf/cdc/VaidyaMS07
fatcat:uydy2haurfg6ndznaewts6oj3a
*to*a finite number*of*linear*inequalities*whose*solutions*define the feasible set*of*stabilizing controllers. ... We provide a proof*of**existence*for a stochastic version*of*such a controller while the deterministic restriction is posed as the*solution**of*a related integer programming problem. ...*Existence**of*a Stochastic Controller The*existence**of*a stochastic controller is linked*to*whether a*solution**exists**to*the set*of**inequalities*given by ∑ i,a R ia P a i j < α ∑ a R ja , j = 1, . . . , ...##
###
Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

2015
*
Mathematical Problems in Engineering
*

The stability

doi:10.1155/2015/502475
fatcat:flbykh4uc5dwxmrg7yqwleej5i
*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. ... The trivial*solution*( ) ≡ 0 (or origin)*of*switched system (1)-(2) is said*to*be stable if for any > 0 there*exists*a = ( ) such that the*inequality*‖ ( , 0 , 0 )‖ < is satisfied for any time > 0 whenever ...##
###
A General Projection Neural Network for Solving Monotone Variational Inequalities and Related Optimization Problems

2004
*
IEEE Transactions on Neural Networks
*

In addition

doi:10.1109/tnn.2004.824252
pmid:15384525
fatcat:rbik6qliznasjaktezv6wberzq
*to*its simple*structure*and low complexity, the proposed neural network includes*existing*neural networks for optimization, such as the projection neural network, the primal-dual neural network ... Furthermore, several improved stability criteria*on*two special cases*of*the general projection neural network are obtained under weaker conditions. ... This property shows that the*existence**of*the equilibrium point*of*(1) is equivalent*to*the*one**of*the*solutions**of*GVI. ...##
###
A Characterization of Lyapunov Inequalities for Stability of Switched Systems

2017
*
IEEE Transactions on Automatic Control
*

Finally, we provide a geometric interpretation

doi:10.1109/tac.2017.2671345
fatcat:oe547cqhvzct5epyjf44x3gkdq
*of*these conditions, in terms*of**existence**of*an invariant set. ... For this purpose, we investigate the*structure**of*sets*of*LMIs that provide a sufficient condition for stability. ... Suppose there*exist**Lyapunov*functions V 1 , . . . , V k ,*one*per node*of*G, that satisfy the*inequalities*imposed by the edges*of*G with γ > 1. ...##
###
Coulomb Control of Nonequilibrium Fixed Shape Triangular Three-Vehicle Cluster

2011
*
Journal of Guidance Control and Dynamics
*

Theorem 2 proves the

doi:10.2514/1.47835
fatcat:oqsqct3ejbfj5hlv7boamdzlda
*existence**of**solutions**to*the*inequalities*in Egs. (41) and (42) unless the condition in Eq. (48) occurs. ... If the following two*inequalities*and*one*equation do not happen at the same time a,b, <0 (48a) arb, <0 (48b) ayb, = a,b, (48c) then for any c € R, there always*exists*a*solution**of*the matrix [A] that ...##
###
Page 3733 of Mathematical Reviews Vol. , Issue 2002E
[page]

2002
*
Mathematical Reviews
*

Necessary and sufficient con- ditions are derived which require the

*Lyapunov*function*to*be nonincreasing only along*one*subsequence*of*the ‘switching’.” ... Summary: “We describe a new proof*of*the well-known*Lyapunov*matrix*inequality*about the location*of*the eigenvalues*of*a matrix in some region*of*the complex plane. ...##
###
Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities

2001
*
IEEE transactions on fuzzy systems
*

Simulation studies, which include an algorithm for

doi:10.1109/91.919248
fatcat:fikjh6ficnbijkg432txzxq234
*solution**of*bilinear matrix*inequalities*, demonstrate the proposed method. ... It is well known, however, that there*exist*stable differential inclusions, hence T-S fuzzy models whose stability is unprovable by a globally quadratic*Lyapunov*function. ...*To*obtain a synthesis result, the state-dependent gain , which, in general, is discontinuous*on*, , requires additional*structure*as well. ...##
###
LaSalle-Yoshizawa Corollaries for Nonsmooth Systems

2013
*
IEEE Transactions on Automatic Control
*

*Lyapunov*-based analysis methods are developed using differential inclusions

*to*achieve asymptotic convergence when the candidate

*Lyapunov*derivative is upper bounded by a negative semi-definite function ... In this note, two generalized corollaries

*to*the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. ... ACKNOWLEDGMENT The authors would like

*to*express their gratitude

*to*Professor A. Teel for his constructive comments during the development

*of*this work. ...

##
###
Synthesis of Lyapunov Functions using Formal Verification
[article]

2021
*
arXiv
*
pre-print

Recent employments

arXiv:2112.01835v1
fatcat:y4erhzxp55cndhodhvl6nudx7q
*of*SMT solvers within the*Lyapunov*function synthesis provided effective tools for automated construction*of**Lyapunov*functions alongside with sound computer-assisted certificates. ... Additionally, we address constructions*of**Lyapunov*functions for state-dependent switching systems. We illustrate our approach by means*of*various examples from the control systems literature. ... If the*inequality*system has no*solution*, the output*of*the check is unsat and no*Lyapunov*function with the given*structure**exists*. ...##
###
Stability of fractional-order nonlinear systems by Lyapunov direct method
[article]

2018
*
arXiv
*
pre-print

Second, we establish fractional

arXiv:1712.02921v2
fatcat:poyrtferrra2pc4ddhkwwrtaeu
*Lyapunov*functions*to*fractional-order systems without the assumption*on*the global*existence**of**solutions*. ... First, we prove an*inequality*concerning the fractional derivatives*of*convex*Lyapunov*functions without the assumption*on*the*existence**of*derivative*of*pseudo-states. ... We also do not require the condition*on*the*existence**of*derivative*to*pseudo-states in the*inequality*concerning the fractional derivatives*of*convex*Lyapunov*functions. ...
« Previous

*Showing results 1 — 15 out of 30,311 results*