Fig. 6. An estimation of the total system convergence speed (body #1 controlled). In summary, a class of composite systems discussed in this paper, which is expected to cover many types of SPS dynamics in the practical sense, has the locally stabilizable structure. And local controllers for this purpose can be designed for small-size subsystems of the grobal dynamical equation. This fact gives the tractability and the flexibility to the SPS controller synthesis, compared with the conventional centralized control approaches. The following discussions are devoted to an approach to estimate the total system's convergence speed. A method is proposed to estimate the convergence speed of the total system, although details are omitted here, by utilizing only the aggregated system's information (4). The chart of Fig. 6 shows one of the results on the total closed-loop system convergence speed estimation, when one local control station is implemented at body #1. It is noted that the uncontrolled body #2 obeys its own convergence speed of -£w, separated from the body #l's controlled convergence speed, as a goes to large. When local controllers are implemented to both of the bodies #1 and #2, the total system's convergence speed approaches to their own designed properties as shown in Fig. 7. The validity of these estimated results has been confirmed by comparing with exact convergence properties obtained by solving the total system's eigenvalues directly.
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