Stability analysis and stabilization synthesis for periodically switched linear systems with uncertainties

This paper addresses the stability analysis and stabilization problems for periodically switched linear systems (PSLSs) with uncertainties in the discrete-time domain. An LMI (linear matrices inequality)-based necessary and sufficient condition is given for the autonomous uncertain PSIS to be asymptotically stable. Then, an LMI-based condition for state feedback stabilization is established. If the condition holds, the computation of feedback gains is also given.