Stability of distributed heterogeneous systems with static nonlinear interconnections

This paper studies the problem of L2 stability of a system with distributed heterogeneous dynamic nodes (or subsystems) that are connected by static nonlinear links. Both the heterogeneities of the subsystems and the nonlinearities of the interconnections are considered. First, a sufficient and necessary condition is given, which shows the equivalence between the L2 stability and an integral quadratic inequality defined by a specially structured operator. Then, under the assumption that the nonlinearities of the interconnections satisfy the sector conditions, an algebraic constraint on the interconnection is established. Based on this, a sufficient condition that the system is finite-gain L2 stable is obtained. For the case of linear time invariant (LTI) subsystems, a frequency domain condition is given, which is numerically solvable by using the Kalman–Yakubovic–Popov (KYP) lemma. Finally, a numerical example is included to demonstrate the use of the results obtained.

Research highlights
► The consideration of both the heterogeneity of the subsystems and the non-idealization of the interconnections.
► The matrix constraint of the nonlinearities of the interconnections.
► The equivalence between the L2 stability and an integral quadratic inequality defined by a specially structured operator.
► The generalized stability criterion of heterogeneous system with non-ideal interconnections.
► The numerically solvable test derived from the KYP lemma.