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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