Abstract
This chapter explores the convergent designs of switched linear systems. A switched linear system is a hybrid/nonlinear system which consists of several linear subsystems and a switching rule that decides which of the subsystems is active at each moment in time. Convergence of nonlinear/hybrid systems is an interesting property, since it results in a limit solution that is independent of the initial conditions of the system. This is useful in synchronization problems. Another possible area of interest is the performance analysis of nonlinear systems. For general nonlinear systems simulation-based analysis is quite impossible, since all possible initial conditions need to be evaluated in order to obtain a reliable analysis. For a convergent system, however, this problem does not exist, since all initial conditions lead to the same limit solution. Therefore simulation can be used to analyze and optimize performance of convergent systems. This motivates studies related to the design of convergent systems.
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