The problem addressed in this paper is the construction of homogeneous polynomial Lyapunov functions for linear systems with time-varying structured uncertainties. A sufficient condition for the existence of a homogeneous polynomial Lyapunov function of given degree is formulated in terms of a Linear Matrix Inequalities (LMI) feasibility problem. This condition turns out to be also necessary in...

the modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system. in the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. the stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the ...

This talk concerns the problem of computing invariant sets for linear systems which are subject to hard input and state constraints. Traditionally, the computation of such sets, and of the corresponding induced Lyapunov functions, is performed by iteratively applying the backward reachability map until convergence to a fixed point is achieved, choosing as initial condition the state constraint ...

We introduce the concept of sos-convex Lyapunov functions for stability analysis of discrete time switched systems. These are polynomial Lyapunov functions that have an algebraic certificate of convexity, and can be efficiently found by semidefinite programming. We show that sos-convex Lyapunov functions are universal (i.e., necessary and sufficient) for stability analysis of switched linear sy...

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete–time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and semi–global practical Lyapunov functions for globally asymptotica...

OBJECTIVES To establish a method for the development of a mathematical model of autonomic activity in gastrointestinal movements and to basically evaluate of the application of the nonlinear analysis method to electrogastrography, we performed feature extraction of electrogastrographic changes in healthy elderly and gastrectomized subjects. METHODS The subjects consisted of 9 healthy elderly ...

Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case ...