A linear time-delay state equation is solved by the proposed shifted Legendre polynomials method. The parameter identification of such a system with time delay is also studied. The system is partitioned into several time intervals. Within a certain time interval, the state and control functions are assumed to be expressed by the shifted Legendre polynomials series. Time-delay differential equations are transformed into a series of algebraic equations of expansion coefficients. An effective algorithm is proposed to solve the time-delay system problem and to estimate the system parameters. Only a small number of leading terms of expansion coefficients is enough to get accurate results. By using such an effective computational algorithm, the calculation procedures are greatly simplified. Thus much computer time is saved.
The Application of Shifted Legendre Polynomials to Time-Delay Systems and Parameter Identification
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Chang, R., and Wang, M. (March 1, 1985). "The Application of Shifted Legendre Polynomials to Time-Delay Systems and Parameter Identification." ASME. J. Dyn. Sys., Meas., Control. March 1985; 107(1): 79–85. https://doi.org/10.1115/1.3140711
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