Model reduction for linear switched systems with autonomous switching

This paper proposes a model reduction algorithm for linear switched systems in continuous-time with autonomous switching. An analytic upper bound on the difference between the responses of the original and the reduced order models is derived. The model reduction algorithm is based on the extension of the idea of balanced truncation. The error bound is a direct extension of the one known for linear systems, and it depends on the singular values of the grammians. The class of linear switched systems considered in this paper includes the well-known class of piecewise-linear systems.