## Definition

The term flexible structure or, briefly, structure has different interpretations and definitions, depending on source and on application. For the purposes of this book we define a structure as a linear system, which is

• finite-dimensional;

• controllable and observable;

• its poles are complex with small real parts; and

• its poles are nonclustered.

Control moment gyros

Beam

Beam

Antenna boom

Figure 1.9. The finite-element model of the International Space Station structure.

Antenna boom

Figure 1.9. The finite-element model of the International Space Station structure.

Based on this definition, we derive many interesting properties of structures and their controllers later in this book.

The above conditions are somehow restrictive, and introduced to justify the mathematical approach used in this book. However, our experience shows that even if these conditions are violated or extended the derived properties still hold. For example, for structures with heavy damping (with larger real parts of complex poles), or with some of the poles close to each other, the analysis results in many cases still apply.

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