In this paper a convex optimization approach to design a robust state feedback control is proposed for DC-DC converter systems with mixed delays. Based on the Lyapunov theory, some required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired cont...

this paper deals with the problem of the state estimation of discrete time nonlinear systems described by Takagi-Sugeno structure where the premise variables are not measurable. The proposed observer design method is based on the use of the second method of Lyapunov and a quadratic function. Based on this procedure two methods are proposed. The convergence conditions of the observer are express...

In this paper, the path tracking (PT) control for automatic steering of vehicles is studied. The Takagi–Sugeno (T–S) fuzzy model of vehicle obtained from a nonlinear model is considered and a fuzzy controller is designed. The stability analysis is discussed using Lyapunov’s approach combined with the linear matrix inequalities (LMI) approach. Finally, simulation results are given to demonstrate...

We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : Rn → R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems. A notion of Karush–Kuhn–Tucker polynomials is introduced in a glob...

This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily ...

This paper studies the problem of delay-range-dependent stability for continuous-time system with interval delay. Based on the dividing of the delay and reciprocally convex combination technique, some new delaydependent stability conditions are derived by constructing a novel Lyapunov functional. These criteria are expressed as a set of linear matrix inequalities (LMIs), which can be checked us...

Considering the uncertain discrete time systems of Linear Parameter Varying (LPV) type, in this paper an approach for the synthesis of robust Proporcional+Integral Observers (PIO) is presented. From LPV systems characterized with polytopical uncertainties, the method of design is based on considering a dynamics extended of the typical PIO, in order to transform the design of the matrices of the...

This paper focuses on the problem of switched static output feedback (SOF) control for discrete-time switched linear systems under arbitrary switching laws. The considered class of systems is characterized by a particular structure of system matrices. Our principle idea is addressed in the derivation of new sufficient linear matrix inequalities conditions for the synthesis of a switched control...

A parametric description of static output feedback stabililizing controllers for diffusion systems with Markovian switching is presented. This description is expressed in terms of coupled linear matrix equations and non-convex quadratic matrix inequalities which depend on parameter matrices similar to weight matrices in LQR theory. A convexifying approximation technique is proposed to obtain th...

This note provides another proof for the convexity (strict convexity) of log det(I + KX) over the positive definite cone for any given positive semidefinite matrix K 0 (positive definite matrix K ≻ 0) and the strictly convexity of log det(K + X) over the positive definite cone for any given K 0. Equivalent optimization representation with linear matrix inequalities (LMIs) for the functions log ...