This paper presents a design method for a linear anti-windup filter with filter pole constraints. The anti-windup design problem can be cast as an LMI optimization problem. The anti-windup filter is optimized for L2 performance while its poles are constrained in a predefined region. The constrained poles ensure the fast recovery of saturation free linear responses and practical implementation o...

Stability A globally asymptotically stable equilibrium is a state with the property that all solutions converge to this state, with no large excursions. Stabilization A system is stabilizable (with respect to a given state) if it is possible to find a feedback law that renders that state a globally asymptotically stable equilibrium. Lyapunov and control-Lyapunov functions A controlLyapunov func...

By incorporating an additional recovery compartment in the SLBS model, a new model, known as the SLBRS model, is proposed in this paper. The qualitative properties of this model are investigated. The result shows that the dynamic behavior of the model is determined by a threshold R0. Specially, virus-free equilibrium is globally asymptotically stable if R0 ≤ 1, whereas the viral equilibrium is ...

Because the latent period and the infectious period of tuberculosis TB are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression SP model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reprod...

Abstract. A mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period, relapse and a saturation incidence rate is investigated. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. By using suitable Lyapunov functionals and LaSalle’s invariance ...

In this paper, an adaptive nonlinear controller is designed for rotor Surface Permanent Magnet Synchronous Motor (SPMSM) drive on the basis of Input-Output Feedback Control (IOFC), and Recursive Least Square (RLS) method. The RLS estimator detects the motor electromechanical parameters, including the motor iron loss resistance online. Moreover, a Sliding-Mode (SM) observer is developed for onli...

We formulate a homogeneous model and a stage-structured model for the interactive wild mosquitoes and mosquitoes carrying genetically-modified bacteria. We establish conditions for the existence and stability of fixed points for both models. We show that a unique positive fixed point exists and is asymptotically stable if the two boundary fixed points are both unstable. The unique positive fixe...

In this paper we consider the stability of variable step-size Runge-Kutta methods approximating bounded, stable, and time-dependent solutions of ordinary differential equation initial value problems. We use Lyapunov exponent theory to determine conditions on the maximum allowable step-size that guarantees the numerical solution of an asymptotically decaying time-dependent linear problem also de...

We consider a (deterministic) evolutionary model where players have dynamic expectations about the strategy distribution. We provide a global analysis of the co-evolution of play and expectations for a generic two–by–two game. Besides the the typical indeterminacy of the evolutionary dynamics, we find some other ones: for any initial strategy configuration the dynamics can converge to any asymp...

This paper presents a novel mathematical model with multidrug-resistant MDR and undetected TB cases. The theoretical analysis indicates that the disease-free equilibrium is globally asymptotically stable if R0 < 1; otherwise, the system may exist a locally asymptotically stable endemic equilibrium. The model is also used to simulate and predict TB epidemic in Guangdong. The results imply that o...