In this paper we develop a BMI based method for nonlinear robust stabilization. Robustness against model uncertainty is handled. The development is based on an uncertain multi-model representation of the plant, and an associated piecewise aane state-feedback structure. Assuming a quadratic Liapunov function, a BMI condition for robust (quadratic) stabilization is found. Control constraints are ...

The paper is concerned with the improvement of sufficient conditions for the exponential stability of Hopfield-type neural networks displaying interaction delays. The results are based on a method obtained in our previous work that combines an idea suggested by Malkin for studying the absolute stability of a nonlinear system via their linearisations and a procedure proposed by Kharitonov for co...

Modern aircraft control systems contain the so-called rate limiter elements which are in fact incorporating the saturation function which is a bounded nonlinearity. In certain critical cases the so-called sector rotation a standard procedure in absolute stability leads to the fact that the sector conditions are broken outside a bounded domain. In order to apply standard results of the absolute ...

Within the Liapunov framework, a sufficient condition for uniform asymptotic stability of ordinary differential equations is proposed. Unlike with classical Liapunov theory, the time derivative of the V -function, taken along solutions of the system, may have positive and negative values. It is shown that the proposed condition is useful for the study of uniform asymptotic stability of homogene...

For uncertain linear systems with complex parameter perturbations of static output feedback type a quadratic Liapunov function of maximal robustness was constructed in [5]. Such Liapunov functions can be used to ensure the stability of uncertain systems under arbitrary nonlinear and time-varying perturbations which are smaller than the stability radius. In this paper we establish analogous resu...

For nonlinear input systems of general form, we prove that bounded-input bounded-state stability is equivalent to the existence of a time-dependent Liapunov function which is not necessarily continuous.

In this paper, we consider a contact problem between viscoelastic Bresse beam and deformable obstacle. The well-known normal compliance condition is used to model the contact. existence of unique solution continuous proved using Faedo-Galerkin method. An exponential decay property also obtained defining an adequate Liapunov function. Then, finite element method implicit Euler scheme, approximat...