A 69-year-old woman developed acute pain in the left trigeminal and glossopharyngeal nerve distributions. MR imaging demonstrated a left lateral medullary infarction (LMI) involving the left spinotrigeminal nucleus and tract, nucleus ambiguus, and solitary nucleus. Most patients presenting with trigeminal neuralgia will have disease involving the trigeminal nerve or ganglion or the primary sens...

In this paper, the linear matrix inequality (LMI) conditions for output feedback control problems are presented. The underlying theory is based upon the necessary and sufficient conditions for static output feedback quadratic stabilizability of continuous time-invariant polytopic systems. The proposed two computationally simple LMI-based algorithms (the V-K iterative and non-iterative one) are ...

In this paper, the delay-dependent stability problem for a class of neural networks of neutral-type with interval time-varying delays and nonlinear perturbations is investigated. A novel stability criterion is obtained in terms of linear matrix inequality (LMI) by employing a Lyapunov-Krasovskii functional. The proposed criteria can be checked easily by the LMI Control Toolbox in Matlab. In add...

Linear matrix inequalities (LMIs) prove to be a useful tool for solving several analysis and design problems in linear systems control. However, LMI techniques have mainly been used conjointly with state-space methods. The aim of this paper is to survey several recent achievements that tend to prove that LMI feasibility and optimization problems also arise when dealing with control problems for...

This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constr...

In this paper, the robust observer-based control for a class of uncertain linear systems is considered. Exponential stabilizability for systems is studied and the convergence rate of system is given. Linear matrix inequality (LMI) approach is used to design the feedback control. The control and observer gains are given from the LMI formulations. A numerical example is given to illustrate our re...

Linear quadratic regulator (LQR) with trajectory sensitivity minimization and structurally constrained controller was formulated in [2] and [4]. In these works, a gradient search method, which is a particular type of nonlinear programming, was used to solve the problem. In this paper, we propose a linear matrix inequality (LMI)-based method for the problem. This LMI is formulated with block-dia...

Necessary and suucient conditions are formulated for the zeros of an arbitrary polynomial matrix to belong to a given region D of the complex plane. The conditions stem from a general optimization methodology mixing LFRs, rank-one LMIs and the S-procedure. They are expressed as an LMI feasibility problem that can be tackled with widespread powerful interior-point methods. Most importantly, the ...

We consider the general nonconvex quadratic programming problem and provide a series of convex positive semidefinite programs (or LMI relaxations) whose sequence of optimal values is monotone and converges to the optimal value of the original problem. It improves and includes as a special case the well-known Shor’s LMI formulation. Often, the optimal value is obtained at some particular early r...

This paper focuses on the chaos control problem of the unified chaotic systems with structured uncertainties. Applying Schur-complement and some matrix manipulation techniques, the controlled uncertain unified chaotic system is then transformed into the linear matrix inequality LMI form. Based on Lyapunov stability theory and linear matrix inequality LMI formulation, a simple linear feedback co...