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Observer synthesis under time-varying sampling for Lipschitz nonlinear systems. (English) Zbl 1375.93049

Summary: In this work, the problem of observation of continuous-time nonlinear Lipschitz systems under time-varying discrete measurements is considered. This class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation. Since the network introduces variations in the sampling time, the observer must be designed so that it takes them into account. Here impulsive observers, which make instantaneous correction when information is received, are investigated. Moreover, we consider time-varying observer gains adapting to the varying sampling interval. In order to deal with both continuous-time and discrete-time dynamics, a new hybrid model is used to state the problem and establish the convergence of the proposed observer. First, generic conditions are provided using a hybrid Lyapunov function. Then, a restriction of the generic Lyapunov function is used to establish tractable conditions that allows the analysis and synthesis of an impulsive gain.

MSC:

93B50 Synthesis problems
93C57 Sampled-data control/observation systems
93C62 Digital control/observation systems
93C10 Nonlinear systems in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)

Software:

Sostools; SeDuMi
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References:

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