Stability analysis and model order reduction of coupled systems

Abstract

In this paper we discuss the stability and model order reduction of coupled linear timeinvariant descriptor systems. Sufficient conditions for the asymptotic stability of a closed-loop system are given. We present a model reduction approach for coupled systems based on reducing the order of the subsystems and coupling the reduced-order models through the same interconnection relations as for the original system. Such an approach allows us to obtain error bounds for the reduced-order closed-loop system in terms of the errors in the reduced-order subsystems. Model reduction of coupled systems with unstable or improper subsystems is also considered. Numerical examples are given.

Stability preserving model reduction for linearly coupled linear time‐invariant systems

“…From results of Reis and Stykel [2], we find the upper bound for the H ∞ -error from reducing subsystems by BRBT in the coupled system (1).…”

“…Here, we assume the matrices E i to be nonsingular and that the matrix pencils A i − λE i are stable. The LTI system (1) can be written [2] as…”

“…The authors prove (Corollary 2.3 in [2]) the following sufficient condition for stability of the coupled system (2).…”

“…Moreover, we want to preserve the interconnection structure by only reducing the subsystems, while also preserving the stability of the coupled system. We extend the stability preserving model reduction method for multi-agent systems from [1] to coupled systems considered in [2].…”

Network structure preserving model reduction with weak a priori structural information

“…To preserve structure in the strong sense, balanced truncation was developed in [15], [8], [17], [12], [15]. A priori knowledge of system structure is reflected by the availability of a structured realization of the system, which is any realization of the system that conforms to the structure F l (N, G) with G block diagonal.…”