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顾毓科学论文集（三）1

THEORY OF NONLINEAR CONTROL6

INTRODUCTION6

THREE STAGES IN THE STUDY OF PHYSICAL SYSTEMS7

LINEARIZATION TECHNIQUES9

THE PHASE-SPACE METHOD AND RELATED CONCEPTS11

NEW ANALYTIC TECHNIQUES AND NEW TRANSFORMS14

THEORY OF NON-LINEAR SYSTEMS18

CONCLUDING REMARKS20

REFERNCES21

DLSCUSSION33

TAYLOR-CAUCHY TRANSFORMS FOR ANALY-SIS OF A CLASS OF NONLINEAR SYSTEMS41

Ⅰ.INTRODUCTION42

Ⅱ.RESTRICTIONS ON SYSTEM44

Ⅲ.DESCRIPTION OF THE METHOD47

Ⅳ.THE TAYLOR-CAUCHY TRANSFORM:TTS PROPERTIES AND DERIVATION49

Ⅴ.OPERATIONAL PROPERTIES52

Ⅵ.EXAMPLES OF TAYLOR-CAUCHY TRANSFORM PAIRS53

Ⅵ.APPLICATION OF TAYLOR-CAUCHY TRANS-FORM TOSOLUTION OF NONLINEAR DIFFERENTIAL 　65

Ⅶ.CONCLUSION AND COMMENTS69

LAURENT-CAUCHY TRANSFONMS FOR ANALYSIS OF LINEAR SYSTEMS DESCRIBED BY DIFFERENTIAL DIFFERENCE75

Ⅰ.INTRODUCTION77

Ⅱ.DERIVATION OF THE LAURENT-CAUCHY TRANS-FORM FROM THE TAYLOR-CAUCHY TRANSFORM78

Ⅲ.RESTRICTIONS ON THE FCNCTIONS AND NOTATION81

Ⅳ.APPLICATION OF THE LAURENT-CAUCHY TRANSFORM METHOD83

Ⅴ.COMPUTER CONTROLLED FEEDBACK SYSTEM86

Ⅵ.DERTVATION OF PRODUCT AND SUM TRANSFORMS89

Ⅶ.SUMMATION THEOREMS92

Ⅷ.EXAMPLES94

Ⅸ.COMPARISON OF LAURENT-CAUCHY AND TAYLOR-CAUCHY TRANSFORMS95

Ⅹ.CONCLUSION AND DISCUSSION97

Ⅺ.ACKNOWLEDGMENT98

ON A SYSTEMATIC APPROXIMATION TO THE PARTITION METHOD FOR ANALYSIS OF A CLASS OF NONL INEAR SYSTEMS105

DEVELOPMENT OF METHOD108

APPROXIMATE SOLUTION109

MATHEMATICALLY SPECIFIED FORCING FUNCTION112

ELIMINATION OF EXTRANEOUS SOLUTIONS114

CHANGING THE INTERVAL H115

STARTINCPROCEDURE116

ACCURACY OF APPRONIMATE SOLUTION117

ESTIMATION OF TRUNCATION ERRORS120

DETERMINATION OF INTERVAL H123

APPLICATION OF METHOD124

SECOND-ORDER SERVO WTTH SATURABLE ELEMENT127

COMPARLSON WTTH THE MEIHODS OF NAUMOV AND STOUT133

CONCLUSLONS135

REFERENCES136

ON NONLINEAR NETWORKS WTTH RANDOM INPUTS139

Ⅰ.INTRODUCTION139

Ⅱ.REPRESENTATION OFA ONLINEAR NETWORK140

Ⅲ.A SIMPLE PARTTTION THEORY143

Ⅳ.ANSLYSIS BY THE PARTTIION MEIHOD147

Ⅴ.THE TRANSFORM-ENSEMBLE METHOD150

Ⅵ.WIENER'S THEORY OF NONLINEAR SYSTEMS156

Ⅶ.OTHER THEORETICAL CONTRIBUTIONS164

Ⅷ.COMBINATION OF THE TWO APPROACHES169

Ⅸ.A SUGGESTED UNIFIED APPROACH176

Ⅹ.CONCLUDING REMARKS AND ACKNKWLEDGMENT179

LYAPUNOV APPROACH TO STABILITY AND PERFORMANCE OF NONLINEAR CONTROL SYSTEMS181

THE SECOND OF LYAPUNOV182

TRANSFORMATION TO CANONICAL FORM185

ACKNOWLEDGMENTS193

REFERENCES193

ON NONLINEAR OSCILLATIONS IN ELECTROMECHANICAL SYSTEMS195

PART Ⅰ197

PART Ⅱ203

PART Ⅲ208

CONCLUSIONS218

APPENDIX Ⅰ220

1.HURWTTZ CHARACTER OF THE LECENDRE AND HERMITE POL YNOMIALS224

APPENDIX Ⅱ224

TAYLOR-CAUCHY TRANSFORMS FOR ANALYSIS OF VARYING-PARAMETER SYSTEMS230

NETWORK SYNTHESIS USING LEGENDRE AND HERMITE POLYNOMIALS243

2.PLOTS OF TRANSFER FUNCTIONS AND CROUP DELAY CHARACTERISTICS255

3.HICHER ORDER POLYNOMIAL NETWORK EXAMPLE260

4.SYNTHESIS OF LOSSLESS TRANSMISSION NETWORKS262

5.TANSIENT ANALYSIS OF THIRD ORDER LEGENDRE NETWORK266

6.AMPLTTUDE FREQUENCY RESPONSE MEASUREMENTS269

A NEW METHOD FOR EVALUATING THE DESCRIBING FUNCTION OF HYSTERESIS-TYPE NONLINEARITIES276

INTRODUCTION277

A NEW APPROACH280

CONSTRUCTION OF OUTPUT CONTOUR C284

EXAMPLES FOR CONSTRUCTING CONTOURC288

CONSTRUCTION OF OUTPUT CONTOUR C290

EXAMPLE FOR BACKLASH296

CONCLUSION296

REFERENCES297

ACKNOWLEDGMENT297

PARTITION OF THE PHASE SPACE AS CRITERION FOR ATABILITY AND PERFORMANCE OF NONLINEAR CONTROL SYSTEMS301

1.LYAPUNOVS SECOND METHOD FOR NONLINEAR CONTROL SYSTEMS302

2. A LACRANGIAN FUNCTION OF THE BASIC SYSTEM304

3.ENVELOPE TO LAGRANGIAN FUNCTION AS A LYAPUNOV FUNCTION306

4.H-FUNCTION CRITERION AND THE PARTTTION OF PHASE SPACE307

5.OPTIMIXATION OF A NONLINEARLY DAMPED CONTROL SYSTEM309

6.STABILITY OF NONLINEAR DISCRETE CONTROLLED SYSTEMS313

ANALYSIS OF PARAMETRICALLY EXCITED SYSTEMS323

PART1 PARAMETRIC EXCTTATION WRRH TIME-VARYING ELEMENTS326

PART2 PARAMETRIC EXCTTATION WTTH NONLINEAR ELEMENTS341

SUBHARMONICS IN A VAN DER POL OSCILLATING CIRCUIT359

COMPARISON OF FORCED AND RELAXATION OSCILLATIONS364

ANALYSIS OF SUBHARMONIC OSCILLATIONS366

APPENDIX PERIOD OF RELAXATION372

FORMULATION OF LIAPUNOV FUNCTIONS379

OF NONLINEAR379

ON LIAPUNOV FUNCTIONS OF HIGH ORDER NONLINEAR SYSTEMS396

STABILITY AND DESIGN OF NONLINEAR CONTROL419

PARTⅠ STABILIIY STUDY VIA LIAPUNOV CRTTERION426

PARTⅡ DESIGN OF NONLINEAR CONTROL SYSTEMS VIA LIAPUNOV CRTTERION440

LYAPUNOV FUNCTION OF A FOURTH-ORDER SYSTEM462

ON STABILITY OF SOME FOURTH-ORDER NONLINEAR SYSTEMS WITH FORCING FUNCTIONS475

ON TOPOLOGICAL APPROACHES TO NETWORK THEORY510

SEPARATION OF SINGULARITY REGIONS FOR PHASE TRAJECTORIES IN CERTAIN NONLINEAR SYSTEMS530

EXTENSION OF POPOU'S THEOREMS FOR STABILITY OF NONLINEAR547

STABILITY AND BOUNDEDNESS CONSIDE-RAT6IONS IN SOME NONLINEAR SYSTEMS572

VOLTERRA-WIENER FUNCTIONALS FOR THE ANALYSIS OF NONLINEAR SYSTEMS590