Positive observer design for switched positive T-S fuzzy delayed systems with dwell time constraints

In this paper, the positive observer design problem is investigated for switched positive Takagi-Sugeno (T-S) fuzzy delayed systems (SPFDSs) with dwell time constraints. First, by using a clock-dependent co-positive Lyapunov-Krasovskii function (CDCLKF), sufficient conditions are derived for stability of SPFDSs with dwell time. Then, the observer design problem of SPFDSs is separately considered for the measurable and unmeasurable premise variable cases. On the basis of the obtained stability results, sufficient conditions are presented to check the existence of observers for SPFDSs with measurable and unmeasurable premise variables. Through minimizing the system matrix norm of the error dynamics, the optimized observer gains for SPFDSs with unmeasurable premise variables are achieved, and the errors between the system states and their estimations are reduced. All the clock-dependent conditions are relaxed into sum of squares (SOS) program via the SOS approximation approach. At last, two examples are given to show the validity of our results.