顾毓科学论文集（三） 1
THEORY OF NONLINEAR CONTROL 6
INTRODUCTION 6
THREE STAGES IN THE STUDY OF PHYSICAL SYSTEMS 7
LINEARIZATION TECHNIQUES 9
THE PHASE-SPACE METHOD AND RELATED CONCEPTS 11
NEW ANALYTIC TECHNIQUES AND NEW TRANSFORMS 14
THEORY OF NON-LINEAR SYSTEMS 18
CONCLUDING REMARKS 20
REFERNCES 21
DLSCUSSION 33
TAYLOR-CAUCHY TRANSFORMS FOR ANALY-SIS OF A CLASS OF NONLINEAR SYSTEMS 41
Ⅰ.INTRODUCTION 42
Ⅱ.RESTRICTIONS ON SYSTEM 44
Ⅲ.DESCRIPTION OF THE METHOD 47
Ⅳ.THE TAYLOR-CAUCHY TRANSFORM:TTS PROPERTIES AND DERIVATION 49
Ⅴ.OPERATIONAL PROPERTIES 52
Ⅵ.EXAMPLES OF TAYLOR-CAUCHY TRANSFORM PAIRS 53
Ⅵ.APPLICATION OF TAYLOR-CAUCHY TRANS-FORM TOSOLUTION OF NONLINEAR DIFFERENTIAL 65
Ⅶ.CONCLUSION AND COMMENTS 69
LAURENT-CAUCHY TRANSFONMS FOR ANALYSIS OF LINEAR SYSTEMS DESCRIBED BY DIFFERENTIAL DIFFERENCE 75
Ⅰ.INTRODUCTION 77
Ⅱ.DERIVATION OF THE LAURENT-CAUCHY TRANS-FORM FROM THE TAYLOR-CAUCHY TRANSFORM 78
Ⅲ.RESTRICTIONS ON THE FCNCTIONS AND NOTATION 81
Ⅳ.APPLICATION OF THE LAURENT-CAUCHY TRANSFORM METHOD 83
Ⅴ.COMPUTER CONTROLLED FEEDBACK SYSTEM 86
Ⅵ.DERTVATION OF PRODUCT AND SUM TRANSFORMS 89
Ⅶ.SUMMATION THEOREMS 92
Ⅷ.EXAMPLES 94
Ⅸ.COMPARISON OF LAURENT-CAUCHY AND TAYLOR-CAUCHY TRANSFORMS 95
Ⅹ.CONCLUSION AND DISCUSSION 97
Ⅺ.ACKNOWLEDGMENT 98
ON A SYSTEMATIC APPROXIMATION TO THE PARTITION METHOD FOR ANALYSIS OF A CLASS OF NONL INEAR SYSTEMS 105
DEVELOPMENT OF METHOD 108
APPROXIMATE SOLUTION 109
MATHEMATICALLY SPECIFIED FORCING FUNCTION 112
ELIMINATION OF EXTRANEOUS SOLUTIONS 114
CHANGING THE INTERVAL H 115
STARTINCPROCEDURE 116
ACCURACY OF APPRONIMATE SOLUTION 117
ESTIMATION OF TRUNCATION ERRORS 120
DETERMINATION OF INTERVAL H 123
APPLICATION OF METHOD 124
SECOND-ORDER SERVO WTTH SATURABLE ELEMENT 127
COMPARLSON WTTH THE MEIHODS OF NAUMOV AND STOUT 133
CONCLUSLONS 135
REFERENCES 136
ON NONLINEAR NETWORKS WTTH RANDOM INPUTS 139
Ⅰ.INTRODUCTION 139
Ⅱ.REPRESENTATION OFA ONLINEAR NETWORK 140
Ⅲ.A SIMPLE PARTTTION THEORY 143
Ⅳ.ANSLYSIS BY THE PARTTIION MEIHOD 147
Ⅴ.THE TRANSFORM-ENSEMBLE METHOD 150
Ⅵ.WIENER'S THEORY OF NONLINEAR SYSTEMS 156
Ⅶ.OTHER THEORETICAL CONTRIBUTIONS 164
Ⅷ.COMBINATION OF THE TWO APPROACHES 169
Ⅸ.A SUGGESTED UNIFIED APPROACH 176
Ⅹ.CONCLUDING REMARKS AND ACKNKWLEDGMENT 179
LYAPUNOV APPROACH TO STABILITY AND PERFORMANCE OF NONLINEAR CONTROL SYSTEMS 181
THE SECOND OF LYAPUNOV 182
TRANSFORMATION TO CANONICAL FORM 185
ACKNOWLEDGMENTS 193
REFERENCES 193
ON NONLINEAR OSCILLATIONS IN ELECTROMECHANICAL SYSTEMS 195
PART Ⅰ 197
PART Ⅱ 203
PART Ⅲ 208
CONCLUSIONS 218
APPENDIX Ⅰ 220
1.HURWTTZ CHARACTER OF THE LECENDRE AND HERMITE POL YNOMIALS 224
APPENDIX Ⅱ 224
TAYLOR-CAUCHY TRANSFORMS FOR ANALYSIS OF VARYING-PARAMETER SYSTEMS 230
NETWORK SYNTHESIS USING LEGENDRE AND HERMITE POLYNOMIALS 243
2.PLOTS OF TRANSFER FUNCTIONS AND CROUP DELAY CHARACTERISTICS 255
3.HICHER ORDER POLYNOMIAL NETWORK EXAMPLE 260
4.SYNTHESIS OF LOSSLESS TRANSMISSION NETWORKS 262
5.TANSIENT ANALYSIS OF THIRD ORDER LEGENDRE NETWORK 266
6.AMPLTTUDE FREQUENCY RESPONSE MEASUREMENTS 269
A NEW METHOD FOR EVALUATING THE DESCRIBING FUNCTION OF HYSTERESIS-TYPE NONLINEARITIES 276
INTRODUCTION 277
A NEW APPROACH 280
CONSTRUCTION OF OUTPUT CONTOUR C 284
EXAMPLES FOR CONSTRUCTING CONTOURC 288
CONSTRUCTION OF OUTPUT CONTOUR C 290
EXAMPLE FOR BACKLASH 296
CONCLUSION 296
REFERENCES 297
ACKNOWLEDGMENT 297
PARTITION OF THE PHASE SPACE AS CRITERION FOR ATABILITY AND PERFORMANCE OF NONLINEAR CONTROL SYSTEMS 301
1.LYAPUNOVS SECOND METHOD FOR NONLINEAR CONTROL SYSTEMS 302
2. A LACRANGIAN FUNCTION OF THE BASIC SYSTEM 304
3.ENVELOPE TO LAGRANGIAN FUNCTION AS A LYAPUNOV FUNCTION 306
4.H-FUNCTION CRITERION AND THE PARTTTION OF PHASE SPACE 307
5.OPTIMIXATION OF A NONLINEARLY DAMPED CONTROL SYSTEM 309
6.STABILITY OF NONLINEAR DISCRETE CONTROLLED SYSTEMS 313
ANALYSIS OF PARAMETRICALLY EXCITED SYSTEMS 323
PART1 PARAMETRIC EXCTTATION WRRH TIME-VARYING ELEMENTS 326
PART2 PARAMETRIC EXCTTATION WTTH NONLINEAR ELEMENTS 341
SUBHARMONICS IN A VAN DER POL OSCILLATING CIRCUIT 359
COMPARISON OF FORCED AND RELAXATION OSCILLATIONS 364
ANALYSIS OF SUBHARMONIC OSCILLATIONS 366
APPENDIX PERIOD OF RELAXATION 372
FORMULATION OF LIAPUNOV FUNCTIONS 379
OF NONLINEAR 379
ON LIAPUNOV FUNCTIONS OF HIGH ORDER NONLINEAR SYSTEMS 396
STABILITY AND DESIGN OF NONLINEAR CONTROL 419
PARTⅠ STABILIIY STUDY VIA LIAPUNOV CRTTERION 426
PARTⅡ DESIGN OF NONLINEAR CONTROL SYSTEMS VIA LIAPUNOV CRTTERION 440
LYAPUNOV FUNCTION OF A FOURTH-ORDER SYSTEM 462
ON STABILITY OF SOME FOURTH-ORDER NONLINEAR SYSTEMS WITH FORCING FUNCTIONS 475
ON TOPOLOGICAL APPROACHES TO NETWORK THEORY 510
SEPARATION OF SINGULARITY REGIONS FOR PHASE TRAJECTORIES IN CERTAIN NONLINEAR SYSTEMS 530
EXTENSION OF POPOU'S THEOREMS FOR STABILITY OF NONLINEAR 547
STABILITY AND BOUNDEDNESS CONSIDE-RAT6IONS IN SOME NONLINEAR SYSTEMS 572
VOLTERRA-WIENER FUNCTIONALS FOR THE ANALYSIS OF NONLINEAR SYSTEMS 590