H _∞ control of a class of discrete-time Markov jump linear systems with piecewise-constant TPs subject to average dwell time switching

The problem of _∞ control for a class of discrete-time Markov jump linear systems (MJLSs) characterized by piecewise-constant transition probabilities (TPs) is investigated in the paper. The so-called piecewise-constant TPs mean that the TPs are varying but invariant within an interval. The variation of the TPs considered here is subject to a typical class of slow switching signal, the average dwell time (ADT) switching, i.e., the number of switches in a finite interval is bounded and the average time between two consecutive switchings of TP matrices is not less than a constant. In this paper, the technique is illustrated and its use is exemplified with application to the popular class of multiplier-accelerator macroeconomic model.