In this paper Kharitonov's t h e o m for the robust stability of interval polynomials is proved using the second method of Lyapunov. The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. It is shown that if the four Hemite matrices correspondii to the four Kharitonov extreme polynomials are positive definite, the Hermite...

Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multiobjective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lypaunov f...

In this study, the stabilization for the Takagi-Sugeno (T-S) fuzzy discrete system with constrained controls is investigated. The derived stabilization conditions are based on the Lyapunov stability criterion with the piecewise quadratic Lyapunov function. The constrained control inputs are used to assess the possible state transition, following which the stabilization conditions are reduced. T...

In this paper we deal with the problem of computing Lyapunov functions for stability verification of differential systems. We concern on symbolic methods and start the discussion with a classical quantifier elimination model for computing Lyapunov functions in a given polynomial form, especially in quadratic forms. Then we propose a new semi-algebraic method by making advantage of the local pro...

This paper deals with Takagi-Sugeno (T-S) systems stabilization based on dynamic output feedback compensators (DOFC). In fact, only few results consider DOFC for T-S systems and most of them propose quadratic Lyapunov stability function to provide stability conditions, which may lead to conservatism. In this work, to overcome this drawback and enhance the closed-loop transient response, we prov...

In this paper we consider Lur'e systems where a linear dynamical system is feedback interconnected to a multilayer perceptron nonlinearity, corresponding to recurrent neural networks with two hidden layers. For this class of nonlinear systems, we present suu-cient conditions for global asymptotic stability based on quadratic and Lur'e-Postnikov Lyapunov functions. Suucient conditions for dissip...

This paper is concerned with non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models. The well-known problem of handling time-derivatives of membership functions (MFs) as to obtain conditions in the form of linear matrix inequalities (LMIs) is overcome by reducing global goals to the estimation of a region of attraction. Instead of parallel distributed compensation (PDC), a non...

In the paper a theoretical analysis is given for the smallest ball that covers a finite number of points p1, p2, · · · , pN ∈ R . Several fundamental properties of the smallest enclosing ball are described and proved. Particularly, it is proved that the k-circumscribing enclosing ball with smallest k is the smallest enclosing ball, which dramatically reduces a possible large number of computati...

the modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system. in the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. the stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the ...

This paper addresses the problem of robust state estimation of switched uncertain systems subject to unknown disturbances. The proposed approach is based on switched interval observers which provide guaranteed lower and upper bounds allowing to evaluate the set of admissible values of the real state vector. The stability and cooperativity conditions of the proposed switched observer are express...