Observability and Controllability of General Linear Systems treats five different families of the linear systems, three of which are new. The book begins with the definition of time together with a brief description of its crucial properties. It presents further new results on matrices, on polynomial matrices, on matrix polynomials, on rational matrices, and on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the proofs of the new necessary and sufficient observability and controllability conditions for all five classes of the studied systems.
Features
Generalizes the state space concept and the complex domain fundamentals of the control systems unknown in previously published books by other authors.
Addresses the knowledge and ability necessary to overcome the crucial lacunae of the existing control theory and drawbacks of its applications.
Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems.
Upgrades, completes and broadens the control theory related to the classical self-contained control concepts: observability and controllability.
Provides information necessary to create and teach advanced inherently upgraded control courses.
| Preface |
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xi | |
| I System Classes |
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1 | (92) |
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3 | (16) |
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3 | (3) |
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1.2 Notational preliminaries |
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6 | (2) |
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1.3 Compact, simple, and elegant calculus |
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8 | (1) |
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9 | (7) |
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16 | (3) |
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19 | (12) |
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2.1 IO system mathematical model |
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19 | (9) |
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19 | (3) |
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22 | (6) |
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2.2 IO plant desired regime |
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28 | (2) |
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30 | (1) |
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31 | (10) |
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3.1 ISO system mathematical model |
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31 | (7) |
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31 | (2) |
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33 | (5) |
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3.2 ISO plant desired regime |
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38 | (2) |
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40 | (1) |
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41 | (24) |
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4.1 EISO system mathematical model |
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41 | (21) |
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41 | (6) |
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47 | (15) |
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4.2 EISO plant desired regime |
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62 | (2) |
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64 | (1) |
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65 | (12) |
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5.1 HISO system mathematical model |
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65 | (1) |
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65 | (1) |
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65 | (1) |
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5.2 The HISO plant desired regime |
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66 | (8) |
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74 | (3) |
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77 | (16) |
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6.1 IIO system mathematical model |
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77 | (13) |
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77 | (2) |
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79 | (11) |
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6.2 IIO plant desired regime |
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90 | (1) |
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91 | (2) |
| II Observability |
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93 | (64) |
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7 Mathematical preliminaries |
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95 | (38) |
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7.1 Linear independence and matrices |
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95 | (2) |
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7.2 Matrix range, null space, and rank |
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97 | (7) |
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7.3 Linear independence and scalar functions |
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104 | (3) |
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7.4 Linear independence and matrix functions |
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107 | (13) |
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7.5 Polynomial matrices. Matrix polynomials |
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120 | (5) |
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125 | (8) |
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8 Observability and stability |
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133 | (10) |
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8.1 Observability and system regime |
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133 | (1) |
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8.2 Observability definition in general |
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134 | (2) |
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8.3 Observability criterion in general |
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136 | (3) |
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8.4 Observability and stability |
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139 | (4) |
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139 | (2) |
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8.4.2 System stability and observability |
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141 | (2) |
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9 Various systems observability |
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143 | (14) |
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9.1 IO systems observability |
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143 | (4) |
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9.2 ISO systems observability |
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147 | (2) |
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9.3 EISO systems observability |
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149 | (1) |
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9.4 HISO systems observability |
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150 | (2) |
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9.5 IIO systems observability |
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152 | (5) |
| III Controllability |
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157 | (70) |
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10 Controllability fundamentals |
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159 | (12) |
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10.1 Controllability and system regime |
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159 | (1) |
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10.2 Controllability concepts |
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159 | (1) |
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10.3 Controllability definitions in general |
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160 | (2) |
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10.4 General state controllability criteria |
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162 | (3) |
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10.5 General output controllability criteria |
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165 | (6) |
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11 Various systems controllability |
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171 | (56) |
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11.1 IO system state controllability |
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171 | (14) |
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171 | (1) |
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172 | (13) |
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11.2 IO system output controllability |
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185 | (10) |
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185 | (1) |
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185 | (10) |
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11.3 ISO system state controllability |
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195 | (2) |
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195 | (1) |
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196 | (1) |
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11.4 ISO system output controllability |
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197 | (4) |
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197 | (1) |
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197 | (4) |
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11.5 EISO system state controllability |
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201 | (2) |
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201 | (1) |
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201 | (2) |
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11.6 EISO system output controllability |
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203 | (3) |
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203 | (1) |
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203 | (3) |
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11.7 HISO system state controllability |
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206 | (4) |
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206 | (1) |
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207 | (3) |
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11.8 HISO system output controllability |
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210 | (4) |
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210 | (1) |
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210 | (4) |
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11.9 IIO system state controllability |
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214 | (8) |
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214 | (2) |
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216 | (6) |
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11.10 IIO system output controllability |
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222 | (7) |
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222 | (1) |
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222 | (5) |
| IV Appendix |
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227 | (100) |
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229 | (14) |
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229 | (1) |
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230 | (1) |
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230 | (1) |
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230 | (1) |
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230 | (9) |
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A.3.1 Calligraphic Letters |
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231 | (1) |
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231 | (2) |
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233 | (1) |
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234 | (5) |
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239 | (1) |
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A.5 Symbols, vectors, sets and matrices |
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240 | (1) |
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241 | (2) |
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243 | (6) |
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243 | (6) |
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249 | (6) |
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C.1 Transformation of IO into ISO system |
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249 | (2) |
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C.2 ISO and EISO forms of HO system |
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251 | (4) |
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255 | (72) |
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255 | (1) |
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256 | (2) |
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258 | (12) |
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270 | (3) |
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273 | (3) |
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276 | (1) |
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277 | (2) |
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279 | (1) |
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280 | (2) |
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D.10 Proof of Theorem 161 |
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282 | (12) |
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D.11 Proof of Theorem 163 |
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294 | (10) |
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D.12 Proof of Theorem 173 |
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304 | (3) |
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D.13 Proof of Theorem 181 |
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307 | (2) |
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D.14 Proof of Theorem 185 |
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309 | (5) |
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D.15 Proof of Theorem 215 |
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314 | (13) |
| V Index |
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327 | |
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329 | (2) |
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331 | |
Mr. Lyubomir T. Gruyitch is Certified Mechanical Engineer (Dipl. M. Eng.), Master of Electrical Engineering Sciences (M. E. E. Sc.), and Doctor of Engineering Sciences (D. Sc.) (All with the University of Belgrade, Serbia). Dr. Gruyitch was a leading contributor to the creation of the research Laboratory of Automatic Control, Mechatronics, Manufacturing Engineering and Systems Engineering of the National School of Engineers (Belfort, France), and a founder of the educational and research Laboratory of Automatic Control of the FME. He has published 13 books (in: English 12, Serb 1), 4 textbooks (in: Serb), 11 lecture notes (in: English 2, French 7, Serb 2), one manual of solved problems (in: Serb), one book translation from Russian, chapters in eight scientific books, 130 scientific papers in scientific journals, 173 conference research papers and two educational papers. Professor Gruyitch supervised one doctorate at the University of Technology Belfort-Montbeliard - UTBM (France), which gained the highest grade by an international (French - USA) jury, five doctorates at the University of Belgrade (Serbia), four DEA (equivalent to M. Sc.) theses at the ENI and five master theses at the University of Belgrade. Professor Gruyitch was a co-initiator of the proposal for a new tentative, highly advanced, Department of Automatique et Systémique at the UTBM, and the Coordinator of the team that worked out the full project. He was cofounder of the Cathedra of Automatic Control and of the undergraduate and graduate Group of Automatic Control of the FME. He introduced a number of new courses at the universities in France, South Africa and Serbia. He was the principal investigator supervising several projects funded by industry in Serbia. Professor Gruyitch was a member of the Acting Senate of the UTBM and the Coordinator of the Commission of Research of the UTBM. He was the Chief of the Cathedra of Automatic Control, the Chief of the Laboratory of Automatic Control and the President of the Senate of the Faculty of Mechanical Engineering, Belgrade. Dr. Gruyitch gave invited university seminars in Belgium, Canada, England, France, Russia, Serbia, Tunis and USA. He was invited plenary sessions speaker, Organizer and/or Chairman of invited sessions at the international conferences, and President of the International Program Committee of the IFAC - IFIP - IMACS Conference Control of Industrial Systems, Belfort, France (more than 300 participants from 42 countries with four continents).
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