Stabilizing design for switched linear control systems: a constructive approach

摘要

In this paper, we develop a unified constructive design approach for continuous-time/discrete-time switched linear control systems, which is analogous to the standard design mechanism of linear time-invariant systems. First, we prove that any switched linear system admits a system canonical decomposition with clear controllability structures. Then, we show that any controllable single-input switched linear system can be converted into a normal form by means of a state feedback transformation and a co-ordinate change, while a controllable multi-input system is feedback reducible to a controllable single-input system via non-regular state feedback. Next, based on the system normal form, we present constructive design procedures for quadratic and non-quadratic feedback stabilization for switched linear control systems. Finally, illustrative examples are carried out to exhibit the effectiveness of the proposed design method.