Stability analysis of hybrid composite dynamical systems: Descriptions involving operators and differential equations

We address the stability analysis of composite hybrid dynamical feedback systems of the type depicted in Fig. 1, consisting of a block (usually the plant) which is described by an operator
L
and of a finite-dimensional block described by a system of ordinary differential equations (usually the controller). We establish results for the well-posedness, attractivity, asymptotic stability, uniform boundedness, asymptotic stability in the large, and exponential stability in the large for such systems. The hypotheses of these results are phrased in terms of the I/O properties of
L
and in terms of the Lyapunov stability properties of the subsystem described by the indicated ordinary differential equations. The applicability of our results is demonstrated by means of general specific examples (involving C
0
-semigroups, partial differential equations, or integral equations which determine
L
).