Farkas’ lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebraic certificates for all infeasible linear matrix inequalities in the spirit of real algebraic geometry. Mor...

this paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space takagi-sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. lyapunov krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

in this paper, linear matrix inequality (lmi) approach for synchronization of chaotic fuzzy cellular neural networks (fcnns) with discrete and unbounded distributed delays based on sampled-data controlis investigated. lyapunov-krasovskii functional combining with the input delay approach as well as the free-weighting matrix approach are employed to derive several sufficient criteria in terms of...

Quadratic programming (QP) is an optimization problem wherein one minimizes (or maximizes) a quadratic function of a finite number of decision variable subject to a finite number of linear inequality and/ or equality constraints. In this paper, a quadratic programming problem (FFQP) is considered in which all cost coefficients, constraints coefficients, and right hand side are characterized by ...

In this paper we study frequency dependent error bounds for comparison and simpliication of models with uncertainty. The uncertainty is described by quadratic constraints and the error bounds are calculated based on solutions to linear matrix inequalities.