Stability and Tracking Recovery of Continuous-Time Markov Jump Piecewise Affine Systems Using Virtual-Sensor-Based Reconfiguration

This technical note studies both the stability and tracking recovery problems for a class of continuous-time Markov jump piecewise-affine systems against sensor faults. A novel reconfigurable control design approach is proposed to recover the mean-square input-to-state stability of the closed-loop system and the tracking property of constant reference inputs, the key idea of this approach is to insert a reconfiguration block including a separate virtual sensor between the faulty system and the nominal controller. Then, a novel extended improved mode-region switching paths (extended-IMRSPs) algorithm is developed to overcome the state switching position mismatch between the faulty system and the reconfiguration block due to interleaving different regions. Furthermore, the
$\mathbb {S}$
-procedure is employed to cope with the affine term, combining with the ellipsoidal outer approximation technique. Finally, the effectiveness and the advantage of both the proposed reconfigurable control strategy and the developed extended-IMRSPs algorithm are demonstrated via an illustrative example.