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...

The problem of robust stability analysis for uncertain discrete singular time-delay systems is investigated in this paper. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time-delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncerta...

This paper deals with several challenging problems of robust filtering for two-dimensional (2-D) systems. First of all, new linear matrix inequality (LMI) characterizations for the and 2 norms of 2-D systems are introduced and thoroughly established. Based on these preparatory results, convex (LMI) characterizations for robust , 2, and robust mixed 2 filtering are derived. The efficiency and vi...

This paper presents a methodology for the design of proportional-derivativetype anti-windup compensators (PDAWCs) for linear time-invariant systems with input and output saturation nonlinearities. A linear matrix inequality (LMI) condition for a closed-loop control system representation is given to take into account the nonlinearities and disturbance. A PDAWC is designed by solving the LMI prob...

In this paper, under the assumption that the activation functions only satisfy global Lipschitz conditions, a novel LMI-based sufficient condition for global asymptotic stability of equilibrium point of a class of BAM neural networks with reaction–diffusion terms and distributed delays is obtained by using degree theory, LMI method, inequalities technique and constructing Lyapunov functionals. ...

This paper considers the problem of local reliable control for continuous-time linear systems with saturating actuators and disturbance. The local stability and the performance of the designed closed-loop system is guaranteed not only when all control components are operational, but also in case of actuator outages in the preselected subset of actuators. Linear matrix inequality (LMI) method an...

In this paper, the problem of dynamics analysis for a class of new impulsive stochastic Cohen–Grossberg neural networks with Markovian jumping and mixed time delays is researched. Some criteria for the asymptotical stability in mean square are obtained based on linear matrix inequality (LMI) forms, which can be easily solved by LMI Toolbox in Matlab. An example is given to show the effectivenes...

2.3. H∞ Performance 3. Controller Design Using Linear Matrix Inequalities 3.1. Linearizing Change of Variables – State Feedback 3.2. Linearizing Change of Variables Output Feedback 3.3. LMI Approach to Multiobjective Design 3.4. Existence of Solutions and Conservatism of Design 4. Illustrative Design Example: Robust Control of a Power System Stabilizer 4.1. Problem Description 4.2. Design Speci...