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A controllable system is not necessarily output controllable. For example, if matrix D = 0 and matrix C does not have full row rank, then some positions of the output are masked by the limiting structure of the output matrix, and therefore unachievable. Moreover, even though the system can be moved to any state in finite time, there may be some ...
More properties of controllable systems can be found in Chen (1999, p. 145), as well as the proof for the other equivalent statements of “The pair (,) is controllable” presented in section Controllability in LTI Systems.
Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. In control theory, the observability and controllability of a linear system are mathematical duals.
A variable in an experiment which is held constant in order to assess the relationship between multiple variables [a], is a control variable. [2] [3] A control variable is an element that is not changed throughout an experiment because its unchanging state allows better understanding of the relationship between the other variables being tested.
A variable may be thought to alter the dependent or independent variables, but may not actually be the focus of the experiment. So that the variable will be kept constant or monitored to try to minimize its effect on the experiment. Such variables may be designated as either a "controlled variable", "control variable", or "fixed variable".
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In that paper the relation to solvability of the Lur’e equations was also established. Both papers considered scalar-input systems. The constraint on the control dimensionality was removed in 1964 by Gantmakher and Yakubovich [3] and independently by Vasile Mihai Popov. [4] Extensive reviews of the topic can be found in [5] and in Chapter 3 ...
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