The problem addressed in this paper is the construction of homogeneous polynomial Lyapunov functions for linear systems with time-varying structured uncertainties. A sufficient condition for the existence of a homogeneous polynomial Lyapunov function of given degree is formulated in terms of a Linear Matrix Inequalities (LMI) feasibility problem. This condition turns out to be also necessary in...

Positive polynomial matrices and linear matrix inequalities (LMI) can be used to design linear parameter varying (LPV) controllers depending polynomially on the scheduling parameters, and robust to polynomial parametric uncertainty. The salient features of the approach are (a) the ability to design a controller of order and structure fixed a priori; (b) the use of a transfer function, or polyno...

Abstract—This paper investigates the problem of H∞ static output feedback (SOF) control for discrete-time switched linear systems with average dwell time switching. By using the multiple Lyapunov function technique, a switched SOF controller is designed such that the closed-loop system is exponentially stable and achieves a weighted L2-gain. Sufficient conditions for SOF control are derived and...

This paper deals with the problem of absolute stability of neutral type Lur’e systems with time-varying delays. By constructing new Lyapunov-Krasovskii functional, a matrix-based on quadratic convex approach combining with some improved bounding techniques for integral terms such as Wirtinger-based integral inequality, new stability condition is much less conservative and more general than some...

This paper considers the stability problem of Lur’e type descriptor systems (LDS) with sector and slope restricted nonlinearities. The concepts of global index one and strongly absolute stability are firstly introduced. Then by using S-procedure and matrix inequality approach, two sufficient conditions for LDS to be strongly absolutely stable are derived. It is shown that such conditions also g...

In this paper we derive stabilization conditions for the class of piecewise affine (PWA) systems using the linear matrix inequality (LMI) framework. We take into account the piecewise structure of the system and therefore the matrix inequalities that we solve are less conservative. Using the upper bound of the infinite-horizon quadratic cost as a terminal cost and constructing also a convex ter...

A new model order reduction (MOR) technique is presented which preserves passivity and non-expansivity. It is a projection-based method which exploits the solution of Linear Matrix Inequalities (LMI’s) to generate a descriptor state space format which preserves positive-realness and bounded-realness. In the case of both non-singular and singular systems, solving the LMI can be replaced by equiv...

The problems of delay-dependent exponential passivity analysis and exponential passification of uncertain Markovian jump systems MJSs with partially known transition rates are investigated. In the deterministic model, the time-varying delay is in a given range and the uncertainties are assumed to be norm bounded. With constructing appropriate Lyapunov-Krasovskii functional LKF combining with Je...

This paper presents the problem of decentralized robust control for discrete-time fuzzy bilinear interconnected large-scale system. Based on the Lyapunov criterion and the parallel distribute compensation (PDC) scheme, the sufficient conditions are derived to guarantee the robust stability of the overall fuzzy system via bilinear matrix inequalities (BMIs). The V-K iteration algorithm is employ...

In this paper, passivity analysis of fractional-order neutral-type fuzzy cellular bidirectional associative memory (BAM) neural networks with time-varying delays is investigated. Based on the Lyapunov–Krasovskii functional, delay-dependent sufficient conditions for solvability passive problem are obtained in terms linear matrix inequalities (LMIs), which can be easily checked by using MATLAB LM...