Common Controller Design for a Class of Hybrid Control Systems

For a linear system with multiple linear controllers, the problem of stabilization is to seek proper control inputs and a control law that steer the system exponentially stable. Based on the system canonical decomposition and cyclic matrix theory, a common state-feedback controller is designed to stabilize the system. The proposed controller is always continuous along the switching law, which avoids discontinuity of the control input signal. A numerical example is presented to verify the effectiveness of the proposed scheme.