Quadratic Constraint for Parallel Splitting Systems

Abstract

In this chapter, we consider parallel splitting interconnected systems with a mixed connection structure, as shown in Fig. 3.1. In these subsystems, the coupling vectors $v_i$ and $w_i$ are split into two subcoupling vectors to explicitly describe the serial and parallel splitting connections. Unlike the parallel systems described in the literature of dissipative system theory wherein each input also equals to the common input, see, e.g. [139], here the parallel splitting, or parallelised, systems whose inputs are summed up to a common input as shown in Fig. 3.2.