ΑΝΑΛΥΣΗ ΓΕΝΙΚΕΥΜΕΝΩΝ ΙΔΙΟΜΟΡΦΩΝ ΣΥΣΤΗΜΑΤΩΝ ΑΥΤΟΜΑΤΟΥ ΕΛΕΓΧΟΥ

THE "SMOOTH" SOLUTIONS OF LINEAR HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS (WHICH CORRESPOND TO MULTIVARIABLE SYSTEMS) OR EQUIVALENTLY THE FREE-RESPONSE OF THE SYSTEM (I.E. WHEN THERE IS NO INPUT) CONSISTING OF COMBINATIONS OF EXPONENTIAL MOTIONS HAVE BEEN WELL STUDIED OVER THE PAST DECADES. ONE OF THE CONTRIBUTIONS OF THIS THESIS IS THAT IT PRESENTS A NEW APPROACH OF FINDING THE SMOOTH SOLUTIONS OF THE LINEAR HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS USING THE NOTION OF JORDAN CHAINS FROM THE OPERATOR THEORY. WE ALSO PRESENT A NEW SOLUTION FOR THE INITIAL VALUE PROBLEM AND WE FIND THE COMPATIBILITY CONDITIONS (CONSTRAINTS) THAT THE SYSTEMS' PSEUDO STATES MUST SATISFY IN ORDER THAT THE SOLUTIONS OF THESYSTEM EXIST. POSSIBLY THE MOST IMPORTANT CONTRIBUTION OF THIS THESIS IS PRESENTED IN CHAPTER 4. IN THE FIRST PART OF THIS CHAPTER WE GIVE A CLOSED FORMULA FOR THE SOLUTION OF THE HOMOGENEOUS MATRIX DIFFERENTIAL EQUATION Α(Ρ)Β(Τ)=0 IN TERMS OF FINITE AND INFINITE JORDAN PAIRS OF A(S). IN THE SECOND PART OF THE CHAPTER THE IMPULSIVE SOLUTIONS OF THE EQUATION A(Ρ)Β(Τ)=0 ARE RE-EXAMINED IN THE LIGHT OF THE THEORY OF JORDAN CHAINS THAT CORRESPOND TO INFINITE ELEMENTARY DIVISORS OF THE MATRIX A(S). INFINITE ELEMENTARY DIVISORS OF GENERAL POLYNOMIAL MATRICES IS EXAMINED. IT IS SHOWN THAT IMPULSIVE SOLUTIONS ARE DUE TO JORDAN CHAINS OF A "DUAL" POLYNOMIAL MATRIX THAT CORRESPOND TO INFINITE ELEMENTARY DIVISORS THAT ARE ASSOCIATED WITH THE ORDERS OF "ZEROS AT INFINITY" OF THE ORIGINAL MATRIX. ANOTHER CONTRIBUTION OF THIS THESIS IS THE PRESENTATION IN CHAPTER 5 OF THE REALIZATION THEORY FOR RATIONAL MATRICES USING THE NOTIONS OF FINITE AND INFINITE JORDAN PAIRS. THAT IS, GIVEN THE FINITE AND THE INFINITE JORDAN PAIR OF APOLYNOMIAL MATRIX A(S) WE FIND A MINIMAL REALIZATION FOR ITS INVERSE A-1(S) WHICH IN GENERAL IS A RATIONAL MATRIX. FINALLY ONE OF THE MAIN CONTRIBUTIONS OF THIS THESIS IS ITS TREATMENT OF THE REACHABILITY PROPERTIES OF POLYNOMIAL MATRIXDESCRIPTIONS (PMD'S) USING TIME DOMAIN ANALYSIS IN CHAPTER 7. THERE, AFTER THEEXTENSION OF THE THEORY PRESENTED IN CH. 6 (REGARDING THE REACHABILITY PROPERTIES OF GENERALIZED STATE SPACE SYSTEMS) IN A WAY TO COVER THE MORE GENERAL CASEOF PMD'S, WE PRESENT THE RELATION BETWEEN DECOUPLING ZEROS AT INFINITY OF PMD'S AND THE LAURENT EXPANSION OF THE CORRESPONDING TRANSFER FUNCTION MATRIX.

Grantor dc:publisher

Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

Year dc:date

1990

Author dc:creator

• Φραγκούλης, Γεώργιος

• Differential equations
• GENERALIZED SINGULAR CONTROLSYSTEMS
• Polynomial matrices
• ΑΛΥΣΙΔΕΣ JORDAN ΚΑΙ ΛΥΣΕΙΣ ΔΙΑΦΟΡΙΚΩΝ ΕΞΙΣΩΣΕΩΝ
• ΓΕΝΙΚΕΥΜΕΝΑ ΙΔΙΟΜΟΡΦΑ ΣΥΣΤΗΜΑΤΑ ΕΛΕΓΧΟΥ
• Διαφορικές εξισώσεις
• Πολυωνυμικοί πίνακες
• Φυσικές Επιστήμες
• Natural Sciences
• Μαθηματικά
• Mathematics

Language dc:language

gre

Identifier

10.12681/eadd/1512

OAI identifier oai:identifier

oai:10442/1512