Results 1  10
of
17
LMI tests for positive definite polynomials: Slack variable approach
 IEEE Trans. on Automatic Control
"... The considered problem is assessing nonnegativity of a function’s values when indeterminates are in domains constrained by scalar polynomial inequalities. The tested functions are multiindeterminates polynomial matrices which are required to be positive semidefinite. For such problems new tests b ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
The considered problem is assessing nonnegativity of a function’s values when indeterminates are in domains constrained by scalar polynomial inequalities. The tested functions are multiindeterminates polynomial matrices which are required to be positive semidefinite. For such problems new tests based on linear matrix inequalities are provided in a Slack Variables type approach. The results are compared to those obtained via the SumOfSquares approach, are proved to be equivalent in case of unbounded domains and less conservative if polytopictype bounds are known.
Stability analysis of fluid flows using sumofsquares.
 In Proc. 2010 American Control Conference,
, 2010
"... Abstract This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sumofsquares decomposition ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sumofsquares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended to infinite dimensional NavierStokes systems using robust optimization techniques. Crucially, this extension requires only the solution of infinitedimensional linear eigenvalue problems and finitedimensional sumofsquares optimization problems. We further show that subject to minor technical constraints, a general polynomial Lyapunov function is always guaranteed to provide better results than the classical energy methods in determining a lowerbound on the maximum Reynolds number for which a flow is globally stable, if the flow does remain globally stable for Reynolds numbers at least slightly beyond the energy stability limit. Such polynomial functions can be searched for efficiently using the SOS technique we propose.
Synchronization of Chaotic Systems Using SampledData Polynomial Controller
"... This paper presents the synchronization of two chaotic systems, namely the drive and response chaotic systems, using sampleddata polynomial controllers. The sampleddata polynomial controller is employed to drive the system states of the response chaotic system to follow those of the drive chaotic ..."
Abstract
 Add to MetaCart
(Show Context)
This paper presents the synchronization of two chaotic systems, namely the drive and response chaotic systems, using sampleddata polynomial controllers. The sampleddata polynomial controller is employed to drive the system states of the response chaotic system to follow those of the drive chaotic system. Because of the zeroorderhold unit complicating the system dynamics by introducing discontinuity to the system, it makes the stability analysis difficult. However, the sampleddata polynomial controller can be readily implemented by a digital computer or microcontroller to lower the implementation cost and time. With the sumofsquares (SOS) approach, the system to be handled can be in the form of nonlinear statespace equations with the system matrix depending on system states. Based on the Lyapunov stability theory, SOSbased stability conditions are obtained to guarantee the system stability and realize the chaotic synchronization subject to an H 1 performance function. The solution to the SOSbased stability conditions can be found numerically using the thirdparty Matlab toolbox SOSTOOLS. Simulation examples are given to illustrate the merits of the proposed sampleddata polynomial control approach for chaotic synchronization problems.
Exact Asymptotic Stability Analysis and RegionofAttraction Estimation for Nonlinear Systems
"... We address the problem of asymptotic stability and regionofattraction analysis of nonlinear dynamical systems. A hybrid symbolicnumeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov func ..."
Abstract
 Add to MetaCart
We address the problem of asymptotic stability and regionofattraction analysis of nonlinear dynamical systems. A hybrid symbolicnumeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.
Linear control of timedomain constrained systems
, 2012
"... a b s t r a c t This paper presents a general framework for the design of linear controllers for linear systems subject to timedomain constraints. The design framework exploits sumsofsquares techniques to incorporate the timedomain constraints on closedloop signals and leads to conditions in t ..."
Abstract
 Add to MetaCart
a b s t r a c t This paper presents a general framework for the design of linear controllers for linear systems subject to timedomain constraints. The design framework exploits sumsofsquares techniques to incorporate the timedomain constraints on closedloop signals and leads to conditions in terms of linear matrix inequalities (LMIs). This control design framework offers, in addition to constraint satisfaction, also the possibility of including an optimization objective that can be used to minimize steady state (tracking) errors, to decrease the settling time, to reduce overshoot and so on. The effectiveness of the framework is shown via a numerical example.