Journal ArticleDOI
A new set of orthogonal functions and its application to the analysis of dynamic systems
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It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.Abstract:
The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.read more
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Orthogonal Hybrid Functions (HF) for Solving Second Order Differential Equations using One-Shot Integration Operational Matrices
TL;DR: In this paper, a set of orthogonal hybrid functions (HF) generated from the synthesis of Orthogonal sample-and-hold functions (SHF) and triangular functions (TF) are derived for second-order integration.
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A New Approach to Approximate Solutions of Single Time-Delayed Stochastic Integral Equations via Orthogonal Functions
TL;DR: In this paper , a new numerical method for solving single time-delayed stochastic differential equations via orthogonal functions was proposed, which achieved a O(h2) convergence rate.
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Z Sadati,KH Maleknejad +1 more
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Control of Time-Varying Systems based on Forward Riccati Formulation in Hybrid Functions Domain
TL;DR: In this paper , the state space equation of LTV system is rewritten in the Hybrid functions (HF) domain where results a set of linear discrete equations instead of having a complex Forward-in-time Propagating Riccati Equation (FPRE).
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A new recursive method for the analysis of linear time invariant dynamic systems via double-term triangular functions (DTTF) in state space environment
TL;DR: In this article, a new recursive method for system analysis via double-term triangular functions (DTTF) in state space environment has been presented, which proves to be more accurate as compared to single term Walsh series (STWS) method with respect to mean integral square error (MISE).
References
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Modern control engineering
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Journal ArticleDOI
Zur Theorie der orthogonalen Funktionensysteme
TL;DR: In der Theorie der Reihenentwicklung der reellen Funktionen spielen die sog. orthogonalen Funktionensysteme eine fuhrende Rolle.
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Identification of continuous-time systems
G.P. Rao,Heinz Unbehauen +1 more
TL;DR: Continuous-time model-based system identification as mentioned in this paper is a well-established field in the field of control systems and is concerned with the determination of particular models for systems that are intended for a certain purpose such as control.
Journal ArticleDOI
Walsh operational matrices for fractional calculus and their application to distributed systems
C.F. Cheng,Y.T. Tsay,Tao Wu +2 more
TL;DR: In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.