On Stabilization of Switched Linear MI Systems Using in Part Common Left Eigenvector Assignment Based on LMIs∗

The problem of assigning in part common left eigenvector assignment by the state feedback control of linear multi-input systems is considered in the paper. Based on linear matrix inequalities characterization, the exposition of the problem is formulated to handle a common left eigenvector for switched modes. Limited by preexisting degrees of freedom, which factually makes mutually contingent subsets of the closed-loop eigenvalue spectrum of each mode, the design conditions for in part common left eigenvector assignment of all modes are derived in the terms of linear matrix inequalities. The procedure provides a way available in linear switched control system design while the state-space control structures take standard forms. An example is included to assess the properties of the technique and its application.