4767

4486

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي

1388

[هفت]، 111ص: مصور، جدول، نمودار.

ص. ع. به: فارسي و انگليسي

حميد رضا مرزبان، مرتضي اسماعيلي

88/8/19

مهدي كرباسي، فريد بهرامي

رياضي

ID4486

به فارسي و انگليسي: قابل رؤيت در نسخه ديجيتال

Analysis of Linear Delay Systems Using Hybrid of Block Pulse Functions and Chebyshev Polynomials Maryam Shahsiah Maryam Shahsiah@math iut ac ir April 21 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Hamid Reza Marzban hmarzban@cc iut ac irSupervisor Dr Morteza Esmaeili emorteza@cc iut ac ir2000 MSC Primary 49J25 49K25 34K35 Secondary 93C05 93B99 Key words Chebyshev polynomials Block pulse functions Hybrid functions Delay operational matrix AbstractIn this thesis we present an expanded account of a computational method for nding thesolution of linear time varying delay systems based on articles by M Razzaghi and H R Marzaban 2001 and H R Marzban and M Razzaghi 2004 Also we extend the proposedmethod to solve piecewise constant delay systems For this purpose the operational matrixof delay corresponding to piecewise constant delay systems is constructed Dynamical systems with time delays have received much attention in the past few decades since time delays are frequently encountered in many practical systems such as communi cation networks chemical processes transportation and power systems The presence ofdelays makes analysis and control design much more complicated Time delay systems aretherefore an important class of systems which their analysis has been of interest to manyinvestigators It is well known that it is di cult to analytically solve a time varying delaysystem with piecewise constant delay function several numerical methods have been used toobtain an approximate solution for delay di erential equations Orthogonal functions havebeen applied to solve various problems of dynamic systems Much progress has been madetowards the solution of delay systems Signals frequently have mixed features of continuity and jumps In such situations nei ther the continuous basis functions nor piecewise constant basis functions taken alone wouldform an e cient basis in the representation of such signals The method is based upon hybridof block pulse functions and Chebyshev polynomials The approach is based on expandingvarious time functions in the system as their truncated hybrid functions The associatedoperational matrices of integration product and delay are used to reduce the solution oftime delay systems to the solution of algebraic equations Moreover we introduce the delayoperational matrix of piecewise constant delay systems and apply for solving these systems This matrix contains many zeros hence making the approach computationally very attrac tive It is also shown that the hybrid of block pulse functions and Chebyshev polynomialsprovides an exact solution for the cases when the exact solutions are polynomials Illustrativeexamples are included to demonstrate the validity and applicability of the proposed method The method is easy to implement and yields very accurate results 1

حميد رضا مرزبان، مرتضي اسماعيلي

مهدي كرباسي، فريد بهرامي