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...

The purpose of this paper is to present a tutorial overview of Linear Fkactional Transformations (LFT) and the role of the Structured Singular Value, p, and Linear Matrix Inequalities (LMI) in solving LFT problems.

This paper examines the problem of designing robust H∞ controllers for for HIV/AIDS infection system with dual drug dosages described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H∞ controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for the s...

This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Carathéodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are als...

This paper proposes performance criteria for linear systems with Markovian jumping parameters. Exact convex conditions for internal stability and contractiveness of such systems are expressed in the form of linear matrix inequalities.

This paper discusses the fixed-order robust filtering problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration are assumed to be norm-bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix, respectively. First, a criterion based on linear matrix inequalities is provided for testing...

This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Carathéodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are als...

In this paper we consider discrete-time, linear stochastic systems with random state and input matrices which are subject to stochastic disturbances and controlled by dynamic output feedback. The aim is to develop an H 1-type theory for such systems. For this class of systems a Stochastic Bounded Real Lemma is derived which provides the basis for a Linear Matrix Inequality (LMI) approach simila...