Time-varying gain-scheduling ó-error mean square stabilisation of semi-Markov jump linear systems

In this study, a time-varying gain-scheduling approach is proposed to deal with the problem of stabilisation for a class of semi-Markov jump linear systems. A more general class of Lyapunov functions that depends not only on the system modes, but also on the staying time during the current system mode is constructed, which can cover the common time-invariant Lyapunov functions as special cases. In the sense of the ó-error mean-square stability proposed previously, the numerically testable sufficient criteria for the stability analysis are derived and certain techniques are employed such that the obtained conditions are linear in the system matrices. Both the time-invariant and time-varying control syntheses are investigated, and the results in a recent study can be deemed as extreme cases of the obtained criteria. Finally, the developed theoretical results are verified by three numerical examples, and it is demonstrated that the results based on the time-varying approach is less conservative than those based on the time-invariant method.