Abstract :
Large space structures, or any mechanically flexible structures, are inherently
distributed parameter systems DPSs.whose dynamics are modeled by partial,
rather than ordinary, differential equations. Such DPSs are described by operator
equations on an infinite-dimensional Hilbert or Banach.space. However, any
feedback controller for such a DPS must be a finite-dimensional and discrete-time.
system to be implemented with on-line digital computers and a finite small.
number of actuators and sensors. There are many ways to synthesize such controllers;
we will emphasize the Galerkin or finite-element approach. Although the
overall performance of finite-dimensional controllers is important, the first consideration
is their stability in closed-loop with the actual DPS. The analysis of DPSs
makes use of the theory of semigroups on the infinite-dimensional state space. We
will present stability bounds in both the time and frequency domains for infinite-dimensional
systems. Currently, the frequency domain approach appears to yield
more easily tested stability conditions than the time domain approach; however, we
will show some relationships between these two methods and emphasize the role
played by the DPS semigroup and its properties. It seems to us that such stability
conditions are essential for the planning and successful operation of complex
systems like large aerospace structures
