Fig. 2. A simple example model and its digram. NUMERICAL EXAMPLES AND DISCUSSION Our major concern lies in a linearized lumped-mass mechanical vibration system represented by the 2nd order matrix differential equation; Mw + Dw + Kw = f, where M is a diagonal full rank matrix and D and K are positive semidefinite symmetric matrices. Many dynamical equations required to represent the SPS motions could be reduced to this form by linearization, i.e., lumped-mass finite element models of elastic structures, or flexibly connected rigid bodies. It is proved for this model that local controllers of arbitrary numbers and locations can stabilize the SPS system, and total stability is guaranteed against the variations of the subsystems connection parameters. A detailed discussion on this matter is described in (4). To illustrate this general result, a simple example of a spring-dashpot connected two mass system is considered here (Fig. 2). Figure 2(b) is a digram of the total system including connecting matrices A,2 and A21. By supposing that only one control station is allowed at the body #1, the local controller is designed for the uncoupled system S] separately from the connecting body #2 as shown in Fig. 2(c). Then, the total closed-loop system is constructed by aggregation, and its global stability is evaluated based on this aggregated model. The results of this controller design and stability evaluation procedure is shown in Fig. 3.
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