In this paper, we study the discrete hybrid system with different initial times. By employing Lyapunov-like functions, some new comparison theorems and several practical stability criteria for discrete hybrid system with initial time difference are obtained.

AbstructThe cerebellar model articulation controller (CMAC) neural network is a practical tool for improving existing nonlinear control systems. A typical simulation study is used to clearly demonstrate that the CMAC can effectively reduce tracking error, but can also destabilize a control system which is otherwise stable. Then quantitative studies are presented to search for the cause of insta...

In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the presen...

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear behavior can be found in engineering, management science, econ...

In this paper we discuss the practical stability of a class of time delay systems with an unstable equilibrium. We obtain sufficient conditions based on Lyapunov-Krasovskii functionals stated in terms of the feasibility of LMI’s. A “Practical” exponential estimate of the solution is also obtained. The result is extended to the practical stabilization and to the case of systems with multiple del...

Evaluating plume stability is important for the evaluation of natural attenuation of dissolved chemicals in ground water. When characterizing ground water contaminant plumes, there are numerous methods for evaluating concentration data. Typically, the data are tabulated and ground water concentrations presented on a site figure. Contaminant concentration isopleth maps are typically developed to...

This paper aims to give sufficient conditions for a cascade composed of nonlinear timevarying systems that are uniformly globally practically asymptotically stable (UGPAS) to be UGPAS. These conditions are expressed as relations between the Lyapunov function of the driven subsystem and the interconnection term. Our results generalise previous theorems that establish the uniform global asymptoti...

A tremendous diversity of ligand binding proteins exists in nature. This undoubtedly creates considerable opportunities for scientific and medicinal applications. In this chapter, we will consider a range of ligand binding proteins, with particular attention to two classes, namely the ligand-binding proteins of the bacterial periplasm and odorant-binding proteins, because these proteins are the...

Differential linear repetitive processes evolve over a subset of the upper-right quadrant of the 2D plane where the unique feature is a series of sweeps or passes through a set of dynamics governed by the solution of a linear matrix differential equation over a finite duration t ∈ [0, α] where α is termed the pass length or duration. On each pass an output, termed the pass profile, is produced,...

What does a child’s search of a large, complex cartoon for the eponymous character (Waldo) have to do with Internet routing? Network operators also search complex datasets, but Waldo is the least of their worries. Routing oscillation is a much greater concern. Networks can be designed to avoid routing oscillation, but the approaches so far proposed unnecessarily reduce the configuration flexibi...