Event-triggered finite-time L₁ control for positive Markov jump systems with partly known transition probability

The article studies the event-triggered finite-time L₁ control design for positive Markov jump systems(PMJSs) with partly known transition probability. Firstly, with regard to the unique positive characteristic, a novel 1-norm based event-triggering condition is proposed for PMJSs. Then, sufficient conditions of positivity and finite-time L₁ boundedness are provided for the closed-loop system under the constructed even-triggered control law. Based on this, by applying the matrix decomposition technology to the event-triggered controller gain matrix, an effective mode-dependent event-triggered finite-time L₁ control scheme in the solvable linear programming(LP) form is presented for PMJSs while preserving the positivity and finite-time L₁ boundedness in closed-loop. Further, an effective LP-based event-triggered finite-time L₁ control scheme is also obtained for PMJSs with completely known transition probability and completely unknown transition probability, respectively. Finally, two examples are presented to verify the validity of the obtained results.