A discrete-time population model in which individuals are distributed over a discrete phenotypic trait-space is studied. It is shown that, for an irreducible mutation matrix , if mutation is small, then an interior equilibrium exists, that is globally asymptotically stable in , while for arbitrary large mutation each trait persists uniformly. For the model reduced to only two traits, conditions...

We study the global stability of a class of models for in-vivo virus dynamics that take into account the Cytotoxic T Lymphocyte immune response and display antigenic variation. This class includes a number of models that have been extensively used to model HIV dynamics. We show that models in this class are globally asymptotically stable, under mild hypothesis, by using appropriate Lyapunov fun...

The Integral Input to State Stability (iISS) property is studied is the context of nonlinear time-invariant systems in cascade. Some sufficient conditions for the preservation of the iISS property under a cascade interconnection are presented. Those are first given as growth restrictions on the supply functions of the storage function associated to each subsystem, and then are expressed as solu...

This paper presents a nonlinear controller based on Sontag’s feedback to render the electromechanical valve actuator (EVA) globally asymptotically stable (GAS). Electromechanical valve actuators have received much attention recently due to their potential for improving the performance of the internal combustion engine. Various control schemes for the EVA have been proposed, however stability is...

We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number, R0 is less than unity. We also note that when R0 . 1, the disease-free equilibrium is unstable and the endemic equilibrium i...

This paper proposes a high gain disturbance observer based control approach for nonlinear systems. Compared with previous works, it can admit a much larger class of disturbances produced by nonlinear exo‐systems. Our approach will follow the framework of the two‐stage design procedure, which separates the disturbance observer design from the controller desi...

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform globa...

The dynamical equations for a spinning top are derived in which the orientation is specified by a complex variable using stereographic projection of Poisson’s equations. Necessary and sufficient conditions for Lyapunov stability of the uncontrolled motion of the spinning top are derived using the Energy-Casimir method. Control laws that globally asymptotically stabilize the spinning top to the ...

A class of time-varying and nonlinear discrete systems with random and uncertain parameters is considered. The method of an estimation (evaluation) of the probability or the certainty index that the system is globally asymptotically stable is presented. The estimation consists in the determination of the lower and upper bounds for the probability and the certainty index via the determination of...

We analyze the dynamics of self-organizing cortical maps under the influence of external stimuli. We show that if the map is a contraction, then the system has a unique equilibrium which is globally asymptotically stable; consequently the system acts as a stable encoder of external input stimuli. The system converges to a fixed point representing the steady-state of the neural activity which ha...