This is a tutorial on the mathematical theory and process control applications of linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Many convex inequalities common in process control applications are shown to be LMIs. Proofs are included to familiarize the reader with the mathematics of LMIs and BMIs. LMIs and BMIs are applied to several important process control applic...

In this paper, we consider the problem of global μ-stability for complex-valued neural networks (CVNNs) with unbounded time-varying delays and it has been widely investigated. Under mild conditions, some new sufficient conditions for global μ-stability of considered CVNNs are derived. Moreover, some new sufficient conditions are obtained to ensure the global μ-stability of CVNNs in the form of ...

Linear Matrix Inequalities (LMIs) are now widely used as a convenient tool for solving a signiicant number of control problems. Probably for historical reasons, LMIs have mainly been used conjointly with state-space methods. Several recent works however tend to prove that polynomial (or algebraic) methods can also rely on LMIs. With the help of simple illustrative examples, the purpose of this ...

A wide variety of problems in control system theory fall within the class of parameterized Linear Matrix Inequalities (LMIs), that is, LMIs whose coecients are functions of a parameter conned to a compact set. However, in contrast to LMIs, param-eterized LMI (PLMIs) feasibility problems involve innitely many LMIs hence are very hard to solve. In this paper, we propose several eective relaxation...

in this paper, the problems of robust stabilization and$h_{infty}$ control for uncertain stochastic systems withmultiple time delays represented by the takagi-sugeno (t-s) fuzzymodel have been studied. by constructing a new lyapunov-krasovskiifunctional (lkf) and using the bounding techniques, sufficientconditions for the delay-dependent robust stabilization and $h_{infty}$ control scheme are p...

We study stability criteria for discrete time switching systems. We investigate the structure of sets of LMIs that are a sufficient condition for stability (i.e., such that any switching system which satisfies these LMIs is stable). We provide an exact characterization of these sets. As a corollary, we show that it is PSPACE-complete to recognize whether a particular set of LMIs implies the sta...

Purpose Early diagnosis of leptomeningeal carcinomatosis (LMC) is necessary to improve outcomes of this formidable disease. However, cerebrospinal fluid (CSF) cytology is frequently false negative. We examined whether CSF metabolome profiles can be used to differentiate patients with LMC from patients having a risk for development of LMC. Results A total of 10,905 LMIs were evaluated using PC...