Abstract
The problem of compensating by state feedback the modes of a linear switching system in such a way that it becomes asymptotically stable under arbitrary switching is considered. Two different sufficient conditions for the existence of a family of state feedbacks that, compensating each mode, make the switching system asymptotically stable under arbitrary switching are given. Both conditions are derived from the analysis of the system behavior in terms of eigenvalues and eigenspaces of its modes. In particular, the first one exploits the known fact that stability under arbitrary switching is guaranteed if all modes of the system, beside being Hurwitz or Schur stable, have dynamic matrices which are normal, or equivalently which have a set of orthogonal eigenspaces. The second conditions, exploits the fact that stability under arbitrary switching is guaranteed if all modes of the system, beside being Hurwitz or Schur stable, have dynamic matrices which have the same set of eigenspaces. In both cases, a characterization in terms of equations that involve the coefficients of the dynamic matrices and the input matrices of the modes are given. The case of two-dimensional modes is investigated in details and examples are provided.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
