Abstmct This paper reviews i) the background for the modern Hw control theory, and then ii) how it led to the modern optimization theory such as those using LMIs (linear matrix inequalities) and BMIs (bilinear matrix inequalities). Starting from the simplest sensitivity minimization problem, we give solutions via the Nevalinna-Pick interpolation and the Nehari theorem. The latter lea,ds to a Ri...

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...

Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabil...

The paper considers the problem of model reduction for a class of linear parameterdependent (LPD) systems. Three model reduction approaches: balanced truncation, balanced LQG truncation and gain-scheduledH∞ model reduction, are presented to reduce the dimension of LPD systems. For the former two approaches, conditions to proceed the reduction are given in terms of a finite number of linear matr...

The average consensus in directed network of multi-agent with both switching topology and time-varying delay is studied. An orthogonal matrix is introduced to change the initial system into a reduced dimensional system. Based on linear matrix inequalities (LMIs) technique, a sufficient condition about average consensus problem is proposed. A novel form in terms of LMIs is obtained via taking th...

This paper proves that a certain class of nonconvex matrix inequalities is equivalent to linear matrix inequalities (LMIs) plus a nonconvex rank constraint. From the equivalence, this paper proposes two heuristic algorithms, that is extended linearization algorithms, to solve LMIs with a rank constraint using LMI-based approach. Reliability and efficiency of the algorithms are investigated stat...

In this paper, a new T-S fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay, is presented to address the problems of stability analysis and feedback control. Fuzzy controller is designed based on the parallel distributed compensation (PDC), and with a new Lyapunov function, delay dependent asymptotic stability conditions of the closed-loop system are derived v...

For the time-delay feedback control of chaos synchronization problem, an idea of Lyapunov functional with time-delay decomposition is presented. Some delay-dependent synchronization criteria are formulated in the form of matrix inequalities. The controller gain with maximum allowed timedelay can be achieved by solving a set of linear matrix inequalities (LMIs). A simulation example is given to ...

The paper is concerned with robust stability criteria for Takagi- Sugeno (T-S) fuzzy systems with distributed delays and time delay in the leakage term. By exploiting a model transformation, the system is converted to one of the neutral delay system. Global robust stability result is proposed by a new Lyapunov-Krasovskii functional which takes into account the range of delay and by making use o...

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 ...