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Stability analysis with quadratic Lyapunov functions: Some necessary and sufficient multiplier conditions
- Systems and Control Letters
"... In this paper, we present a condition which is both necessary and sufficient for quadratic stability of an uncertain/nonlinear system. This condition is a linear matrix inequality in the Lyapunov matrix and a multiplier matrix associated with the uncertain/nonlinear terms. It is known that this cond ..."
Abstract
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Cited by 6 (6 self)
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In this paper, we present a condition which is both necessary and sufficient for quadratic stability of an uncertain/nonlinear system. This condition is a linear matrix inequality in the Lyapunov matrix and a multiplier matrix associated with the uncertain/nonlinear terms. It is known that this condition is sufficient for quadratic stability. The main contribution of this paper is to demonstrate that it is also a necessary condition, and hence is not a conservative condition for quadratic stability. 1
A Converse Lyapunov Theorem for Linear Parameter Varying and Linear Switching Systems
- SIAM J. Control & Optim
, 2004
"... We study families of linear time-varying systems, where time-variations have to satisfy restrictions on the dwell time, that is on the minimum distance between discontinuities, as well as on the derivative in between discontinuities. ..."
Abstract
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Cited by 5 (3 self)
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We study families of linear time-varying systems, where time-variations have to satisfy restrictions on the dwell time, that is on the minimum distance between discontinuities, as well as on the derivative in between discontinuities.
Linear Matrix Inequalities in Robust Control - A Brief Survey
"... Control system models must often explicitly incorporate in them uncertainties or perturbations. ..."
Abstract
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Cited by 1 (0 self)
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Control system models must often explicitly incorporate in them uncertainties or perturbations.
GPC-LPV: a predictive LPV controller based on BMIs
, 2005
"... In this paper the authors present a predictive linear parameter varying (LPV) controller based on the GPC controller [1]--[3], for nonlinear systems. The resulting controller is denoted as GPC-LPV. This one has the same structure as a general LPV controller [4]--[7], which has a lineal fractional de ..."
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In this paper the authors present a predictive linear parameter varying (LPV) controller based on the GPC controller [1]--[3], for nonlinear systems. The resulting controller is denoted as GPC-LPV. This one has the same structure as a general LPV controller [4]--[7], which has a lineal fractional dependence on the process signal measurements. Therefore, this controller has the ability of modifying its dynamics depending on measurements leading to a possibly nonlinear controller. That controller is designed in two steps. First, for a given steady state point is obtained a linear GPC using a local model of the nonlinear system around that operating point. And second, using bilinear matrix inequalities (BMIs) the remaining matrices of GPC-LPV are selected in order to achieve some closed loop properties: stability in some operation zone, norm bounding of some input/output channels, maximum settling time, maximum overshoot, etc. This methodology of design can be applied to nonlinear systems which can be embedded in a LPV system using differential inclusion techniques. Finally, the GPC-LPV is applied to the nonlinear model of a liquid-gas separation process.
Stability analysis with quadratic Lyapunov functions: Some necessary and sufficient multiplier conditions
, 2008
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