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...

Abstract: This paper addresses the problem of designing a robust output feedback controller for a class of fuzzy uncertain dynamic systems that guarantees i) the L2gain from an exogenous input to a regulated output is less or equal to a prescribed value and ii) the closed-loop fuzzy system to be quadratically stable within a prespecified LMI stability region. Based on an LMI approach, solutions...

This paper deals with the problem of delay-dependent stability for neural networks with distributed delays. Some new sufficient condition are derived by constructing a novel Lyapunov-Krasovskii functional approach. The criteria are formulated in terms of a set of linear matrix inequalities, this is convenient for numerically checking the system stability using the powerful MATLAB LMI Toolbox. M...

The problem of designing a controller to meet different specifications or deciding that no such controller exists is addressed in this paper by linking three types of tools: the Youla parameterization allows searching for a controller in a convex set; formulations using Linear Matrix Inequalities (LMI) are proposed for different practical specifications; the corresponding convex problem is solv...

This paper presents a fuzzy tracking control design based on H∞ performance for nonlinear systems. The Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Based on the H∞ tracking performance, the nonlinear system output is controlled to track a reference signal, and at the same time the tracking performance is attenuated to a prescribed level. Linear matrix inequalities (L...

A new approach for process controllability analysis by using multiobjective optimisation techniques is proposed. Within the approach, a set of performance specifications, such as minimum control error and input effort with closed-loop pole placement are represented as a set of linear matrix inequalities (LMI). The solution to the LMI conditions can be identified as feasible or infeasible. If th...

This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction o...

This paper deals with the problem of designing state or full-order output feedback H-infinity controllers satisfying an α-stability constraint. A descriptor system approach is adopted to derive linear matrix inequality (LMI) conditions of α-stability and H-infinity performance for linear time-invariant (LTI) systems, under which the multiobjective control laws can be constructed with a mix of H...

Abstract— This paper addresses robust consensus problems among multiple agents with uncertain parameters constrained in a given set. Specifically, the network coefficients are supposed polynomial functions of an uncertain vector constrained in a set described by polynomial inequalities. First, the paper provides a necessary and sufficient condition for robust firstorder consensus based on the e...