Consistency of a time-stepping method for a class of piecewise-linear networks

In this brief, we will study the computation of transient solutions of a class of piecewise- linear (PL) circuits. The network models will be so-called linear complementarity systems, which can be seen as dynamical extensions of the PL modeling structure as proposed by [1]. In particular, the numerical simulation will be based on a time-stepping method using the well-known backward Euler scheme. It will be demonstrated, by means of an example, that this widely applied time-stepping method does not necessarily produce useful output for arbitrary linear dynamical systems with ideal diode characteristics. Next the consistency of the method will be proven for PL networks that can be realized by linear passive circuit elements and ideal diodes by showing that the approximations generated by the method converge to the true solution of the system in a suitable sense. To give such a consistency proof, the fundamental framework developed in [2] is indispensable as it proposes a precise definition of a "solution" of a linear complementarity system and provides conditions under which solutions exist and are unique

Zero forcing sets and controllability of dynamical systems defined on graphs

In this technical note, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established. To illustrate the proposed results, special cases including path, cycle, and complete graphs are discussed. Moreover, as shown for graphs with a tree structure, the proposed results of the present technical note together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases. © 2014 IEEE

Rostskyddsbehandling av takplåt på kulturhistoriskt värdefulla byggnader

Den här boken ger vägledning för bedömningar och välgrundade beslut vid underhåll av målade plåttak. Här behandlas processen, från kulturhistoriska förhållningssätt, identifiering av skador, diagnostisering av orsaker, till val av behandling och planering för underhåll och kontroll