State feedback in linear control theory (Q1587895)

The authors present a survey of the role of system invariants in the analysis and design of linear control systems. More precisely, solvability conditions in terms of the invariants are given for the problems of pole assignment stabilization, linear quadratic regulation and diagonal decoupling in the case of the regular state feedback. The case of nonregular state feedback which is much more complex is also discussed. It is shown that when the skeleton system given by the system invariants is too tight to satisfy the design requirements the use of non-regular feedback may do the job. The authors formulate also some control design problems in terms of the Kronecker invariants of the corresponding matrix pencils.