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We have seen in Chapter 5 that there are many linear systems that are not stable. In this chapter we study the problem of stabilizing an unstable system using an appropriate compensator. Not all systems are stabilizable. We characterize all stabilizable systems and give a parametrization of all compensators that stabilize such systems. An important role is played by identifying a linear system with its graph. As in Chapter 4, we assume that time is discrete.
KeywordsState Space Model Partial Isometry Stable Rank Parallel Projection Strong Representation
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