Real-time lebesgue-sampled model for continuous-time nonlinear systems

Traditional model-based approaches are based on periodic sampling, where the model is discretized with a fixed period. Despite the easiness in analysis and design, periodic sampling may be undesirable from the computation-efficiency point of view. This paper presents the Lebesgue-sampled model (LSM) of continuous-time nonlinear systems, where the state iteration is activated on an “as-needed” basis, but not periodically. We show that the proposed LSM behaves exactly the same as a specific event-triggered feedback system. Thus, the properties of the LSM can be studied through the resulting event-triggered system. We provide sufficient conditions to ensure asymptotic stability and uniformly ultimate boundedness of the LSM. Theoretical bounds are derived to quantify the difference between the states of the LSM and the continuous-time system, for both stable and unstable cases. Systematic methods are developed to design the quantizer. Simulations show that the LSM can dramatically reduce the number of iterations without sacrificing accuracy.