Semistability of switched linear systems with applications to distributed sensor networks: A generating function approach

This paper investigates semistability of discrete-time, switched linear systems under both deterministic and random switching policies. The notion of semistability pertains to a continuum of initial state dependent equilibria and has found wide applications such as consensus problems in multi-agent systems. The main contributions of the paper are three folds. First, we show that exponential semistability on a common equilibrium space is equivalent to output exponential stability of the switched linear system with a suitably defined output, under both arbitrary and random switchings. Further, their convergence rates are shown to be identical. Second, it is shown that output stability and its convergence rates can be efficiently characterized via the recently developed generating function approach. Third, we consider algorithm development and analysis of resource allocation schemes for topologically changing, distributed sensor networks. We formulate an iteration process of such an algorithm as a switched linear system, and characterize its convergence using the obtained semistability results.