Abstract
This chapter presents an analysis of state feedback and its limitations. It also includes the design of state estimators for use when some state variables are not available and the use of state estimates in feedback control. State feedback involves the use of the state vector to compute the control action for specified system dynamics. State variable feedback allows the flexible selection of linear system dynamics. This chapter shows a linear system (A, B, C) with constant state feedback gain matrix K. Using the rules for matrix multiplication, it deduces that the matrix K is m X n so that for a single-input system K is a row vector. The dynamics of the closed-loop system depend on the eigenstructure(eigenvalues and eigenvectors) of the matrix Acl. Thus, the desired system dynamics can be chosen with appropriate choice of the gain matrix K. Using output or state feedback, the poles or eigenvalues of the system can be assigned subject to system-dependent limitations. This is known as pole placement, pole assignment, or poleallocation. This is elucidated in the chapter.
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