2,029 research outputs found
<i>l<sup>p</sup></i> gain bounds for switched adaptive controllers
No full textA class of discrete plants controlled by a switching adaptive strategy is considered, and lp bounds, 1 ≤ p ≤ ∞, are obtained for the closed loop gain relating input and output disturbances to internal signals
Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions
Full text linkState-dependent switched systems characterized by piecewise affine (PWA) dynamics in a polyhedral partition of the state space are considered. Sufficient conditions on the vectors fields such that the solution crosses the common boundaries of the polyhedra are expressed in terms of quadratic inequalities constrained to the polyhedra intersections. A piece-wise quadratic (PWQ) function, not necessarily continuous, is proposed as a candidate Lyapunov function (LF). The sign conditions and the negative jumps at the boundaries are expressed in terms of linear matrix inequalities (LMIs) via cone-copositivity. A sufficient condition for the asymptotic stability of the PWA system is then obtained by finding a PWQ-LF through the solution of a set LMIs. Numerical results with a conewise linear system and an opinion dynamics model show the effectiveness of the proposed approach
The water hammer problem and its numerical analysis
Full text linkThis dissertation involves mathematical models of water flow in a pipeline system. The topic has been studied for a long time, such that water distribution systems have evolved in the past few decades, and mathematical models also evolved from linear to nonlinear models, from incompressible to compressible models and also from systems with infinite space domain to systems with boundary conditions, etc. In my research, I managed to analyze the water flow by a 1d Euler equation with dynamical boundary conditions, where the dynamical boundary conditions are in terms of the valve in the middle of the pipe that can be fast closed, causing hydraulic shock which we call the water hammer inside the pipe. This Euler equation system with dynamical boundary conditions is new and is inspired by switch differential algebraic equations (sDAE) proposed by Prof. Stephan Trenn, which is a system consisting of ordinary differential equations (ODE) and algebraic equations. The valve closing and opening can be modeled as the switching signals of different systems, and accordingly in the partial differential equation (PDE) system they can be modeled as changing boundary conditions. Therefore, throughout my research, I performed the analysis by separating the cases that are before and after the valve closure, both in theoretical and numerical ways
An approximation for nonlinear differential-algebraic equations via singular perturbation theory
Full text linkIn this paper, we study the jumps of nonlinear DAEs caused by inconsistent initial values. First, we propose a simple normal form called the index-1 nonlinear Weierstrass form (INWF) for nonlinear DAEs. Then we generalize the notion of consistency projector introduced in Liberzon and Trenn (2009) for linear DAEs to the nonlinear case. By an example, we compare our proposed nonlinear consistency projectors with two existing consistent initialization methods (one is from the paper Liberzon and Trenn (2012) and the other is given by a MATLAB function) to show that the two existing methods are not coordinate-free, i.e., the consistent points calculated by the two methods are not invariant] under nonlinear coordinates transformations. Next we propose a singular perturbed system approximation for nonlinear DAEs, which is an ordinary differential equation (ODE) with a small perturbation parameter and we show that the solutions of the proposed perturbation system approximate both the jumps resulting from the nonlinear consistency projectors and the (^-solutions of the DAE. At last, we use a numerical simulation of a nonlinear DAE model arising from an electric circuit to illustrate the effectiveness of the proposed singular perturbed system approximation of DAEs.</p
On impulse-free solutions and stability of switched nonlinear differential–algebraic equations
Full text linkIn this paper, we investigate solutions and stability properties of switched nonlinear differential–algebraic equations (DAEs). We introduce a novel concept of solutions, called impulse-free (jump-flow) solutions, and provide a geometric characterization that establishes their existence and uniqueness. This characterization builds upon the impulse-free condition utilized in previous works such as Liberzon and Trenn (2009, 2012), which focused on linear DAEs. However, our formulation extends this condition to nonlinear DAEs. Subsequently, we demonstrate that the stability conditions based on common Lyapunov functions, previously proposed in our work (Chen and Trenn, 2022) (distinct from those in Liberzon and Trenn (2012)), can be effectively applied to switched nonlinear DAEs with high-index models. It is important to note that these models do not conform to the nonlinear Weierstrass form. Additionally, we extend the commutativity stability conditions presented in Mancilla-Aguilar (2000) from switched nonlinear ordinary differential equations to the case of switched nonlinear DAEs. To illustrate the efficacy of the proposed stability conditions, we present simulation results involving switching electrical circuits and provide numerical examples. These examples serve to demonstrate the practical utility of the developed stability criteria in analyzing and understanding the behavior of switched nonlinear DAEs.</p
Ask questions, get sales : close the deak and create long-term relationships / Stephan Schiffman.
No full textIncludes index.v, 168 pages ;In Ask Questions, Get Sales, the author and sales guru Stephan Schiffman helps readers boost their careers to the gold-medal level by teaching them how to strengthen their questioning skills during the sales process. The premise is simple yet effective: In order to be successful, salespeople need to change their mindset from "need-orientated" to "do-orientated". The message of the book centers around six core "do" questions: What do you do? How do you do it? When and where do you do it? Why do you do it that way? Who do you do it with? How can we help you do it better? With this indispensable guide in their briefcase, salespeople will have information at the ready to score big sales over the short term and the long term
Switch observability for homogeneous switched DAEs
No full textS.9355-9360We introduce the notions of switching time observability and switch observability for homogeneous switched differential-algebraic equations (DAEs). In contrast to mode detection, they do not require observability of the individual modes and are thus more suitable for fault detection and identification. Based on results in (Küsters and Trenn, 2017) for switched ordinary differential equations (ODEs), we characterize these notions for homogeneous switched DAEs and propose an observer for switch observable systems.50Nr.
Unemployment Benefits and Unemployment Rates of Low-Skilled and Elder Workers in West Germany: A Search Equilibrium Approach
No full textApproach Author & abstract Download 16 References 1 Citations Related works & more Corrections Author Listed: Launov, Andrey ([email protected]) (University of Kent) Wolff, Joachim ([email protected]) (Institute for Employment Research (IAB), Nuremberg) Klasen, Stephan ([email protected]) (University of Göttingen) Registered: Stephan Klasen Abstract In this paper we investigate whether the extension of the entitlement to unemployment benefits in the mid 80s can explain the increase in the unemployment rates of unskilled and elder workers in western Germany. To answer this question we estimate a version of the Burdett-Mortensen search equilibrium model and analyze how workers’ search behaviour responded to these reforms. We try both nonparametric and fully-parametric estimation methods and identify the cases in which the nonparametric approach cannot be applied. We find that the entitlement reforms are largely responsible for the increase of unemployment among unskilled workers
Unemployment Benefits and Unemployment Rates of Low-Skilled and Elder Workers in West Germany: A Search Equilibrium Approach
No full textApproach Author & abstract Download 16 References 1 Citations Related works & more Corrections Author Listed: Launov, Andrey ([email protected]) (University of Kent) Wolff, Joachim ([email protected]) (Institute for Employment Research (IAB), Nuremberg) Klasen, Stephan ([email protected]) (University of Göttingen) Registered: Stephan Klasen Abstract In this paper we investigate whether the extension of the entitlement to unemployment benefits in the mid 80s can explain the increase in the unemployment rates of unskilled and elder workers in western Germany. To answer this question we estimate a version of the Burdett-Mortensen search equilibrium model and analyze how workers’ search behaviour responded to these reforms. We try both nonparametric and fully-parametric estimation methods and identify the cases in which the nonparametric approach cannot be applied. We find that the entitlement reforms are largely responsible for the increase of unemployment among unskilled workers
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