This paper provides new dilated linear matrix inequality (LMI) characterizations for continuous-time controller synthesis. The dilated LMIs enable us to parametrize controllers without involving the Lyapunov variables in the parametrizations. Taking advantage of this feature, we can readily design multiobjective controllers with non-common Lyapunov variables, whereas we are forced to employ a c...

Purpose – The purpose of this paper is to present the methodology to the robust stability analysis of a vision-based control loop in an uncalibrated environment. The type of uncertainties considered is the parametric uncertainties. The approach adopted in this paper utilizes quadratic Lyapunov function to determine the composite Jacobian matrix and ensures the robust stability using linear matr...

Abstract: This paper considers the analysis and synthesis of a spatially distributed controller for discrete-time spatially interconnected parameter-varying system. The system under consideration has both discrete time and space dynamics. The concept of quadratic separators (Iwasaki and Shibata, 2001), (Chughtai and Werner, 2007) has been extended to compute a measure of worst-case performance ...

The paper deals with the stability properties of linear discrete-time switched systems with polytopic sets of modes. The most classical way of studying the uniform asymptotic stability of such a system is to check for the existence of a quadratic Lyapunov function. It is known from the literature that letting the Lyapunov function depend on the time-varying switching parameter improves the chan...

In this paper we propose an unified construction of Lyapunov functions based on Lur’e type functions that allows us to go from Persidskii’s to pure quadratic functions. Such Lyapunov functions allows the establishment of the absolute stability of nonlinear systems with nonlinearities belonging to given sectors. The sectors can be finite or infinite. An stability criterion is formulated in terms...

This paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for Takagi–Sugeno (TS) systems. This approach is based on the idea of multiple Lyapunov functions together with simple techniques for introducing slack matrices. Unlike some previous approaches based on multiple Lyapunov functions, both the stability and the stabilization condition...

In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dep...

This paper investigates 2D mixed continuous-discrete-time systems whose coefficients are polynomial functions of an uncertain vector constrained into a semialgebraic set. It is shown that a nonconservative linear matrix inequality (LMI) condition for ensuring robust stability can be obtained by introducing complex Lyapunov functions depending polynomially on the uncertain vector and a frequency...

An optimization based method is proposed in this paper for the computation of Lyapunov functions and regions of attractions for nonlinear systems containing polynomial and rational terms. The Lyapunov function is given in a special quadratic form, and the negativity of its derivative is ensured using appropriate LMI conditions. The conservatism of the solution is reduced by utilizing Finsler’s ...

We consider the stability of the feedback connection of a linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program. By generalizing the class of candidate Lyapunov functions we improve on existing results in the literature. A Lyapunov function is constructed via the S-procedure from quadratic constraints established using the Karush-Kuhn-Tuc...