Relaxation oscillations exhibiting more than one time scale arise naturally from many physical systems. This paper proposes a method to numerically integrate large systems of relaxation oscillators. The numerical technique, called the singular limit method, is derived from analysis of relaxation oscillations in the singular limit. In such limit, system evolution gives rise to time instants at w...

This paper presents the design of an additive fault tolerant control for nonlinear time-invariant singularly perturbed systems against actuator faults based on Lyapunov redesign principle. The overall system is reduced into subsystems with fast and slow dynamic behavior using singular perturbation method. The time scale reduction is carried out when the singular perturbation parameter is set to...

This paper presents a necessary and sufficient condition for discrete-time singular Markovian jump linear systems with defective statistics of modes transitions to be regular, causal, and stochastically stable. The static output-feedback stabilization problem for discrete-time singular Markovian jump linear system with defective statistics of modes transitions is studied. Furthermore, the defec...

Oue of (.he key questions to be addressed in t,liis paper is how 1.0 estimate the deterministic input multipulse time series from a noisy respouse of the resonant transfer system iii (.lie case where t.he SNR is low aud the system Q(quality laci.or) of Ihe transfer system is high. By generaliziug the sharp truucabion employed in the standard singular-valuedecomposit.ion(SVD), a tapering window ...

We study a singular Reaction-Diffusion system motivated by a dedicated diffusive predator-prey model system devised in the spatially homogeneous case by Courchamp and Sugihara [2]. The reactive part features a functional response to predation and a singular numerical functional response to predation specifically designed for modeling the introduction of greedy predators into a fragile or insula...

There are countless applications of non-linear systems that incorporate delay and algebraic equations. Despite current improvements in control theory, stochastic actuator defects still pose challenges when it comes to these systems. Furthermore, is not possible measure the states system, uncertainties affect system under investigation, problem becomes even more complex. This paper concerned wit...