Further Results on Exponential Estimates of Markovian Jump Systems With Mode-Dependent Time-Varying Delays

Abstract

which is always negative for values of 1 27:02. Since the reset control system produces crossings with the reset surface with intervals that are lesser than 27.02, then it is not guaranteed that the reset control system be stable in this case. Fig. 5 shows a simulation for this system, comparing closed loop outputs both for the base and the reset control system, for 1 m = 0:1. Using again Proposition 4.1, it can be concluded that the closed-loop reset system is asymptotically stable if reset intervals 1 k , k = 0; 1; ..., are always greater than 1 m = 27:1. Fig. 6 shows a simulation for 1 m = 30, showing that the system is stable in spite that the base system is oscillating. For values of 1m closer to the stability limit the response become increasingly oscillating. V. CONCLUSION Stability conditions dependent on the reset times have been developed for reset control systems. As a result, reset control systems stability is determined by using a time-varying discrete time system describing the evolution of the system after the reset instants. In comparison with previous work, the main contribution has been to include restrictions only at the reset instants, and thus results are less conservative and can be applied to reset systems with both stable and unstable base systems. In addition, the time regularization constant has been used to developed a stabilization result for the case in which the base system is stable. As a result, a lower bound of the reset intervals always exists that guarantee stability of the reset system, if no reset action is performed for reset intervals lower than this bound. Several examples have been analyzed in detail, showing in particular how reset times dependent conditions are less conservative that previous reset systems stability results such as the H condition.

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