Linear matrix inequalities
Herbert Werner · IEE Proceedings - Control Theory and Applications · 2003
Linear matrix inequalities (LMIs) have emerged as a powerful tool for numerically solving control problems that are difficult or impossible to solve analytically. The idea is to express a given problem as an optimisation problem with linear objective and semidefinite constraints, where the constraints involve symmetric matrices that are affine in the decision variables. Once a problem has been expressed in this form, efficient LMI solvers can be used to obtain a numerical solution. This Special Section on LMIs for application in control engineering collects a number of recent results in various fields such as linear parameter-varying (LPV) systems, predictive control, sliding mode control, and applications such as control of networked or interconnected systems and robust design of power system stabilisers