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Observer-based tracking control for switched linear systems with time-varying delay. (English) Zbl 1211.93049
Summary: The issue of observer-based tracking control for switched linear systems with time-varying delay is investigated in this paper. The possibility of designing switching control laws based on measured output is considered when the states are not available. Hysteresis based switching method and single Lyapunov-Krasovskii functional method are utilized to the stability analysis and controller design. By introducing the descriptor system method, the consideration of mixed mode is avoided since $\stackrel{˙}{x}\left(t\right)$ can be seen as state variable, and thus it is not necessary to substitute $\stackrel{˙}{x}\left(t\right)$ everywhere by the right-hand part of the system. The variation-of-constants formula is used to overcome the difficulties caused by the estimation error and exotic disturbance. Free weighting matrix scheme facilitates us to the stability analysis and control synthesis, and the numerical example shows the effectiveness of the proposed design methods.
##### MSC:
 93B51 Design techniques in systems theory 93C05 Linear control systems 93D30 Scalar and vector Lyapunov functions 93B50 Synthesis problems