This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods such as the circle and Popov criteria is explained. Several examples are included to demonstrate the flexibility a...

We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga and Todd's method for linear programming. A worst-case analysis shows that the number of iterations grows as the square root of the problem size, but in practice it appears to grow more slowly. As ...

An H∞ synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shapi...

In this paper is estimated the region of attraction of the nonlinear boost DC-AC converter by Sum of Squares. This is an optimization problem of maximization of the Lyapunov surface subjects to certain strict constraints due to saturation of the control variables of the system and to the composition of the inverter, which is formed from two DC-DC converters with positive voltage.

This paper presents a new stabilization criterion for dynamic systems with parametric uncertainties and delays in control input. Based on the Lyapunov method, the stabilization criterion is derived in terms of matrix inequalities which can be easily solved by efficient convex optimization algorithms. Numerical examples are included to show the effectiveness of the proposed method. 2005 Elsevier...

In the paper, we investigate the delay-aware data transmission in renewable energy aided multi-carrier system. Besides utilizing the local renewables, the transmitter can also purchase grid power. By scheduling the amount of transmitted data (The data are stored in a buffer before transmission), the sub-carrier allocation, and the renewable allocation in each transmission period, the transmitte...

Future wireless communication systems are expected to see an explosion in the wireless traffic which is mainly fueled by mobile video traffic. Due to the time varying and bursty nature of video traffic, wireless systems will see a wider range of fluctuations in their traffic patterns. Therefore, traditional physical layer based algorithms which perform resource allocation under the assumption t...

In order to obtain a reliable estimate of the lifetime of the BaBar drift chamber, a dedicated aging test chamber has been constructed. The working gas mixture is Helium/Isobutane (80/20). After accumulating up to 0.11C/cm charge dose the anode wire showed no appreciable signs of aging, but the field wires showed a small Malter effect. At 0.2C/cm the gas gain dropped B6–9% and the Malter effect...

We propose a generative model for automatic query reformulations from an initial query using the underlying subtopic structure of top ranked retrieved documents. We address three types of query reformulations a) specialization; b) generalization; and c) drift. To test our model we generate the three reformulation variants starting with selected fields from the TREC-8 topics as the initial queri...

Momentum methods play a central role in optimization. Several momentum methods are provably optimal, and all use a technique called estimate sequences to analyze their convergence properties. The technique of estimate sequences has long been considered difficult to understand, leading many researchers to generate alternative, “more intuitive” methods and analyses. In this paper we show there is...