Adaptive self-triggered control for positive Markov systems with switching transition rates

The problem of adaptive self-triggered protocol is addressed for positive switching systems with Markov parameters and incomplete transition rates. By means of the switching transition characteristic, the time-varying transition rates are expanded to offer greater flexibility. Based on the state information at the current triggered instant, an adaptive self-triggered strategy is proposed to calculate the next triggered instant in advance, in which no additional hardware is required. The main novelty lies in constructing a suitable adaptive self-triggered control scheme to realize better dynamic performance, overcoming the difficulty caused by limited network resources. By using the matrix decomposition technology and constructing a linear co-positive Lyapunov function, sufficient conditions are derived to ensure the positivity and exponential stability of the underlying system. Finally, two examples are employed to verify the effectiveness of the theoretical results.