Exponential stability of hybrid systems using a Lyapunov approach is considered in this paper. The continuous part of the hybrid system is described by nonlinear differential equations that depend on a discrete state. The discrete state changes when certain switch sets are reached. By using piecewise quadratic forms of the Lyapunov function candidates, it is shown how the stability conditions c...

Abstract The problem of estimating the Domain of Attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a semi-convex approach based on Linear Matrix Inequalities (LMIs) is proposed. Moreover, for the...

The problem of estimating the domain of attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a semi-convex approach based on Linear Matrix Inequalities (LMIs) is proposed. Moreover, for the case of ...

This paper presents a new approach for the stability analysis of TakagiSugeno (T-S) fuzzy systems. An idea is investigated to use piecewise quadratic Lyapunov function with low amount of computations. This class of Lyapunov function candidates is much richer than the common quadratic Lyapunov function. By exploiting the piecewise continuous Lyapunov function, we derive stability conditions that...

We consider optimizing average queueing delay and average power consumption in a nonpreemptive multi-class M/G/1 queue with dynamic power control that affects instantaneous service rates. Four problems are studied: (1) satisfying per-class average delay constraints; (2) minimizing a separable convex function of average delays subject to per-class delay constraints; (3) minimizing average power ...

The difference and differential equations have played an eminent part in nonlinear dynamics systems, but the last two decades one-dimensional maps are considered forefront of systems optimization transportation problems. In nineteenth century, paved a significant role analyzing phenomena using discrete continuous time interval. Therefore, it is used every branch science such as physics, chemist...

We consider the design criteria of a chemical mixing device based on a chaotic flow, with an emphasis on the steady-state devices. The merit of a reactor, defined as the Q-factor, is related to the physical dimension of the device and the molecular diffusivity of the reactants through the local Lyapunov exponents of the flow. The local Lyapunov exponent can be calculated for any given flow fiel...

This paper shows that Lyapunov-based state feedback controller synthesis for piecewise-affine (PWA) slab systems can be cast as an optimization problem subject to a set of linear matrix inequalities (LMIs) analytically parameterized by a vector. Furthermore, it is shown that continuity of the control inputs at the switchings can be guaranteed by adding equality constraints to the problem withou...

In a wide variety of applications including online advertising, contractual hiring, and wireless scheduling, the controller is constrained by stringent budget constraint on available resources, which are consumed in random amount each action, stochastic feasibility that may impose important operational limitations decision-making. this work, we consider general model to address such problems, w...