Triangular Orthogonal Functions for the Analysis of Continuous Time Systems: Convolution Process in Triangular Function Domain and Its Use in SISO Control System Analysis
Citations
16 citations
Cites background or methods from "Triangular Orthogonal Functions for..."
...Ezzati and Najafalizadeh (2011) applied Chebyshev polynomials for nonlinear Volterra-Fredholm integral equations. In Maleknejad et al. (2003), Legendre wavelet was used to solve linear Fredholm and Volterra integral equations of the second kind....
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...Ezzati and Najafalizadeh (2011) applied Chebyshev polynomials for nonlinear Volterra-Fredholm integral equations....
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...…methods based on different wavelets, such as Legendre and Walsh were designed for analysis of control systems and various related applications (Maleknejad et al., 2003; Yousefi and Razzaghi, 2005), and approximating the solution of integral equations (Deb et al., 2007; Yousefi and Razzaghi, 2005)....
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...Maleknejad and Kajani (2002) proposed piecewise constant basis functions to obtain numerical solution of integro-differential equations....
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...Ezzati and Najafalizadeh (2011) applied Chebyshev polynomials for nonlinear Volterra-Fredholm integral equations. In Maleknejad et al. (2003), Legendre wavelet was used to solve linear Fredholm and Volterra integral equations of the second kind. Solving nonlinear Volterra integral equation of the second kind using Chebyshev polynomials was done in the work of Maleknejad et al. (2007). Several numerical methods based on different wavelets, such as Legendre and Walsh were designed for analysis of control systems and various related applications (Maleknejad et al....
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Additional excerpts
...They build an orthogonal set [DA11] [IBW14]....
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4 citations
Cites background or methods from "Triangular Orthogonal Functions for..."
...Following a similar procedure [4] for the components of the TF set comprised of four members, we integrate each member and express the result of integration, as before, in HF domain....
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...Hybrid Function (HF) : A Combination of SHF and TF [7, 8] We can use a set of sample-and-hold functions and the RHTF set of triangular functions [4] to form a hybrid function set, which we name a...
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...In 2003, orthogonal triangular functions (TF) [2-4] were introduced by Deb et al....
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References
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