Abstract
In this paper, we present a method for finding the solution of the linear multi-delay systems (MDS) by using the hybrid of the Block-Pulse functions and the Bernoulli polynomials. In this approach, the MDS is reduced to a system of linear algebraic equations by expanding various time functions for the hybrid functions and using operational matrices. To demonstrate the validity and the applicability of the technique, some examples are presented.
Highlights
Delays occur frequently in biological, chemical, transportation, electronic, communication, manufacturing and power systems [1]
Time-delay and multi-delay systems are very important classes of systems whose control and optimization have been of interest to many investigators [2]-[5]
The hybrid functions consisting of the combination of the Block-Pulse functions with the Chebyshev polynomials [6], the Legendre polynomials [7] [8], or the Taylor series [9] [10] have been shown to be a mathematical power tool for discretization of selected problems
Summary
Delays occur frequently in biological, chemical, transportation, electronic, communication, manufacturing and power systems [1]. The hybrid functions consisting of the combination of the Block-Pulse functions with the Chebyshev polynomials [6], the Legendre polynomials [7] [8], or the Taylor series [9] [10] have been shown to be a mathematical power tool for discretization of selected problems. For approximating an arbitrary function we use less CPU time by applying the Bernoulli polynomials as compared to the shifted Legendre polynomials. We use the hybrid functions consisting of the combination of the Block-Pulse functions and the Bernoulli polynomials to solve the MDS.
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