A sufficient condition for the stability of large-scale interconnections of N linear time-variant systems is presented. Such a condition represents important extensions to passivity criteria and ensures stability by means of the existence of a positive definite (full-block) matrix P which is a common solution to Lyapunov equations involving a diagonal stacking of the N systems and the interconnection structure matrix. An experimental methodology for the verification of the sufficient condition also is proposed, based on evolutionary computation techniques. Applications of the new stability results are provided through illustrative examples, which are developed using particle swarm optimisation and genetic algorithms. © 2013 Taylor & Francis.