Using a scalar reaction-diffusion equation with drift and a cubic nonlinearity as a simple model problem, we investigate the effect of domain size on stability and bifurcations of steady states. We focus on two parameter regimes, namely the regions where the steady state is convectively or absolutely unstable. In the convective-instability regime, the trivial stationary solution is asymptotical...

This paper presents the problem of nonlinear observer design for a class of time-delay nonlinear systems with uncertainty. The nonlinearity of this class of systems has to satisfy the Lipschitz condition whilst the uncertain term is a bounded function. Various performance indices are analysed to test the stability of the error system when all nonlinear terms satisfying the Lipschitz condition. ...

In this paper, we consider the Schrodinger equation with a mass-supercritical focusing nonlinearity, in exterior of smooth, compact, convex obstacle $\R^{d}$ Dirichlet boundary conditions. We prove that solutions negative energy blow up finite time. Assuming furthermore nonlinearity is energy-subcritical, also (under additional symmetry conditions) blow-up same optimal ground-state criterion th...

This paper addresses the stabilization problem of singularly perturbed systems subject to actuator saturation. A solution in terms of linear matrix inequalities is proposed. The saturation is represented by means of a modified sector nonlinearity. The numerical problems due to the ill conditioning of the system model are avoided using a non-decoupling strategy. Some numerical results are also i...

The contribution of this paper is to propose a systematic approach to the observer design for linear time-varying systems. It is based on the exact rewriting of the original time-varying system into a polytopic linear model (PLM). This transformation uses the sector nonlinearity approach based on the convex polytopic transformation. Then a joint state and parameter observer can be designed for ...

We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations which provides computable monotone sequences that converge to the extremal solutions in a sector generate...

Most fuzzy control papers check LMI or SOS stability conditions in order to prove local stability results of nonlinear systems (Takagi-Sugeno fuzzy models or polynomial fuzzy models via Sector Nonlinearity approach). In case of having into account the shape of the membership functions in a particular region of interest, less conservative stability and stabilization conditions can be easily set ...

The purpose of this work is to design a fuzzy integral controller to force the switching of a bioprocess between two different metabolic states. A continuous baking yeast culture is divided in two sub-models: a respiro-fermentative with ethanol production and a respirative with ethanol consumption. The switching between both different metabolic states is achieved by means of tracking a referenc...

In this paper, a delay-tolerable and anti-windup control synthesis technique is proposed. Longitudinal speed tracking performed by an integrated electric drive (IED) system under the multi-domain constraints of network bandwidth actuator saturation investigated. Controller area (CAN) connected to Internet provide interface for cyber attacks. addition, physical characteristics motor sacrifice ve...