A self-triggered control scheme for Markov jump systems under multiple range performance restrictions

This paper proposes a multi-frequency controller design scheme for Markov jump systems (MJSs) based on the self-triggered strategy in a resource-aware way. Firstly, a derandomization technique is introduced to make sure the transition probability information is included in the finite frequency specification analysis. Then, a self-triggered policy is developed to update the control input of the system via the history measurement. Finally, sufficient conditions are deduced that guarantee the multiple range frequency performances and the reduction of computation and communication occupation for the controlled MJSs, simultanously. The cart- spring system is employed to illustrate the effectiveness of the proposed approach.