Theoretical analysis of balanced truncation for linear switched systems

In this paper we present a theoretical analysis of the model reduction algorithm for linear switched systems from Shaker and Wisniewski (2011, 2009). This algorithm is based on balanced truncation. More precisely, (1) we provide a bound on the approximation error in L2 norm, (2) we provide a system theoretic interpretation of grammians and their singular values, (3) we show that the performance of balanced truncation depends only on the input-output map and not on the choice of the state-space representation. In addition, we also show that quadratic stability and LMI estimates of the L2 gain also depend only on the input-output map.