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Maxwell鏄涓€浣嶅埄鐢ㄧ壒寰佹柟绋嬬殑绯绘暩(sh霉)渚嗗垽鏂风郴绲�(t菕ng)绌�(w臎n)瀹氭€х殑浜篬26]銆� 銆€銆€James Clerk Maxwell鏄涓€鍊�(g猫)灏�(du矛)鍙嶉鎺у埗绯荤当(t菕ng)鐨勭┅(w臎n)瀹氭€ч€�(j矛n)琛岀郴绲�(t菕ng)鍒嗘瀽骞剁櫦(f膩)琛ㄨ珫鏂囩殑浜篬8]銆傚湪浠�1868骞寸殑璜栨枃鈥滆珫瑾�(di脿o)绡€(ji茅)鍣ㄢ€濓紙Maxwell J C.On Governors. Proc. Royal Society of London,vol.16:270-283,1868锛変腑锛屽皫(d菐o)鍑轰簡瑾�(di脿o)绡€(ji茅)鍣ㄧ殑寰垎鏂圭▼锛屽苟鍦ㄥ钩琛￠粸(di菐n)闄勮繎閫�(j矛n)琛岀窔鎬у寲铏曠悊锛屾寚鍑虹┅(w臎n)瀹氭€у彇姹轰簬鐗瑰緛鏂圭▼鐨勬牴鏄惁鍏锋湁璨�(f霉)鐨勫(sh铆)閮ㄣ€傞亥?zh菙n)鏄捐啊鎾愰椆琚�?du矛)涓夐殠寰垎鏂圭▼鎻忚堪鐨凾homson s governor, Jenkin s governor 浠ュ強鍏锋湁浜旈殠寰垎鏂圭▼鐨凪axwell s governor閫�(j矛n)琛屼簡鐮旂┒锛屽苟绲﹀嚭浜嗙郴绲�(t菕ng)鐨勭┅(w臎n)瀹氭€ф浠躲€侻axwell鐨勫伐浣滈枊鍓�(chu脿ng)浜嗘帶鍒剁悊璜栫爺绌剁殑鍏堟渤銆俒9][10] 銆€銆€鍚屼竴鏅�(sh铆)鏈熷湪淇勫湅锛�1872骞葱�.袗.缍粈鑱舵牸鎷夋柉鍩猴紙1831-1895锛変篃灏�(du矛)钂告苯姗�(j墨)鐨勭┅(w臎n)瀹氭€у晱椤岄€�(j矛n)琛屼簡鐮旂┒銆傂�.袗.缍粈鑱舵牸鎷夋柉鍩虹殑璜栨枃鈥滆珫瑾�(di脿o)鏁村櫒鐨勪竴鑸師鐞嗏€�1876骞寸櫦(f膩)琛ㄥ湪娉曞湅绉戝(xu茅)闄㈤櫌鍫�(b脿o)涓娿€傂�.袗.缍粈鑱舵牸鎷夋柉鍩哄悓妯ｅ埄鐢ㄧ窔鎬у寲鏂规硶绨″寲鍟忛锛岀敤绶氭€у井鍒嗘柟绋嬫弿杩扮敱瑾�(di脿o)鏁村皪(du矛)璞″拰瑾�(di脿o)鏁村櫒绲勬垚鐨勭郴绲�(t菕ng)銆傞€欎娇鍟忛澶уぇ绨″寲銆�1878骞葱�.袗.缍粈鑱舵牸鎷夋柉鍩洪倓灏�(du矛)闈炵窔鎬х辜闆诲櫒鍨嬭(di脿o)鏁村櫒閫�(j矛n)琛屼簡鐮旂┒銆傂�.袗.缍粈鑱舵牸鎷夋柉鍩哄湪铇囪伅(li谩n)琚鐐鸿嚜鍕�(d貌ng)瑾�(di脿o)鏁寸悊璜栫殑濂犲熀浜�銆俒23] 銆€銆€Maxwell鏄竴浣嶅ぉ鎵嶇殑绉戝(xu茅)瀹�锛屽湪瑷卞鏂归潰閮芥湁妤甸珮鐨勯€犺銆備粬鍚屾檪(sh铆)閭勬槸鐗╃悊瀛�(xu茅)涓浕纾佺悊璜栫殑鍓�(chu脿ng)绔嬩汉锛堣鍏惰珫鏂団€淎 dynamical theory of the electromagnetic field鈥濓紝1864锛�銆傜洰鍓嶇殑鐮旂┒琛ㄦ槑锛孧axwell浜嬪(sh铆)涓婂湪1863骞�9鏈堝嵆宸插熀鏈畬鎴愪簡鍏舵湁闂�(gu膩n)绌�(w臎n)瀹氭€ф柟闈㈢殑鐮旂┒宸ヤ綔銆俒10] 銆€銆€Maxwell鍦ㄤ粬鐨勮珫鏂囦腑閭勫偓淇冩暩(sh霉)瀛�(xu茅)瀹跺€戠洝蹇湴瑙ｆ焙澶氶爡(xi脿ng)寮忕殑绯绘暩(sh霉)鍚屽闋�(xi脿ng)寮忕殑鏍圭殑闂�(gu膩n)绯荤殑鍟忛銆傜敱浜庝簲娆′互涓婄殑澶氶爡(xi脿ng)寮�?j墨ng)]鏈夌洿鎺ョ殑姹傛牴鍏紡锛岄€欑郸鍒ゆ柗楂橀殠绯荤当(t菕ng)鐨勭┅(w臎n)瀹氭€т唬渚嗕簡鍥伴洠銆俒9] 銆€銆€绱勫湪1875骞达紝Maxwell鎿�(d膩n)浠讳簡鍔嶆⿱Adams Prize鐨勮⿻(p铆ng)鐛�(ji菐ng)濮斿摗銆傞€欓爡(xi脿ng)鍏╁勾涓€娆＄殑鐛�(ji菐ng)鎺堜簣鍦ㄨ┎濮斿摗鏈�(hu矛)鎵€閬哥瀛�(xu茅)涓婚鏂归潰绔�?f脿n)骞嶆窎缃撮鎾愭懝?877骞寸殑Adams Prize鐨勪富椤屾槸鈥滈亱(y霉n)鍕�(d貌ng)鐨勭┅(w臎n)瀹氭€р€�銆侲.J.Routh鍦ㄩ€欓爡(xi脿ng)绔熻辰涓互鍏惰窡鎿�(j霉)澶氶爡(xi脿ng)寮忕殑绯绘暩(sh霉)姹哄畾澶氶爡(xi脿ng)寮忓湪鍙冲崐骞抽潰鐨勬牴鐨勬暩(sh霉)鐩殑璜栨枃濂緱妗傚啝锛圧outh E J.A Treatise on the Stability of Motion.London,U.K.:Macmillan,1877锛�銆俁outh鐨勯€欎竴鎴愭灉鐝�(xi脿n)鍦ㄨ绋辩偤鍕炴柉鍒ゆ摎(j霉)銆俁outh宸ヤ綔鐨勬剰缇╁湪浜庡皣鐣�(d膩ng)鏅�(sh铆)鍚勭ó鏈夐棞(gu膩n)绌�(w臎n)瀹氭€х殑瀛ょ珛鐨勭祼(ji茅)璜栧拰闈炵郴绲�(t菕ng)鐨勭祼(ji茅)鏋滅当(t菕ng)涓€璧蜂締锛岄枊濮嬪缓绔嬫湁闂�(gu膩n)鍕�(d貌ng)鎱�(t脿i)绌�(w臎n)瀹氭€х殑绯荤当(t菕ng)鐞嗚珫銆俒26] 銆€銆€Edward John Routh 1831骞�1鏈�20鏃ュ嚭鐢熷湪鍔犳嬁澶х殑榄佸寳鍏�銆備粬鐖惰Κ鏄竴浣嶅湪Waterloo鏈嶅焦鐨勮嫳鍦嬭粛瀹�銆俁outh 11姝查偅骞村洖鍒拌嫳鍦嬶紝鍦╠e Morgan鎸囧皫(d菐o)涓嬪(xu茅)缈�(x铆)鏁�(sh霉)瀛�(xu茅)銆傚湪鍔嶆⿱?q奴)W缈�(x铆)鐨勭暍妤�(y猫)鑰冭│涓紝浠栫嵅寰楃涓€鍚�銆傚苟寰楀埌浜嗏€淪enior Wrangler鈥濈殑姒(y霉)绋辫櫉(h脿o)銆傦紙Clerk Maxwell鎺掑湪浜嗙浜屼綅銆傜洝绠lerk Maxwell鐣�(d膩ng)鏅�(sh铆)琚ū鐐烘渶鑱版槑鐨勪汉銆傦級鐣㈡キ(y猫)鍚嶳outh闁嬪寰炰簨绉佷汉鏁�(sh霉)瀛�(xu茅)鏁欏斧鐨勫伐浣�銆傚緸1855骞村埌1888骞碦outh鏁欎簡600澶氬悕瀛�(xu茅)鐢�锛屽叾涓湁27浣嶇嵅寰椻€淪Enior Wrangler鈥濈ū铏�(h脿o)銆傚缓绔嬩簡鐒″彲鍖规暤鐨勬キ(y猫)绺俱€俁outh浜�1907骞�6鏈�7鏃ュ幓涓�锛屼韩骞�76姝�銆俒25] 銆€銆€Routh涔嬪悗澶х磩浜屽崄骞达紝1895骞�锛岀憺澹暩(sh霉)瀛�(xu茅)瀹禔. Hurwitz鍦ㄤ笉浜嗚ВRouth宸ヤ綔鐨勬儏娉佷笅锛岀崹(d煤)绔嬬郸鍑轰簡璺熸摎(j霉)澶氶爡(xi脿ng)寮忕殑绯绘暩(sh霉)姹哄畾澶氶爡(xi脿ng)寮忕殑鏍规槸鍚﹂兘鍏锋湁璨�(f霉)瀵�(sh铆)閮ㄧ殑鍙︿竴涓柟娉曪紙Hurwitz A. On the conditions under which an equation has only roots with negative real parts. Mathematische Annelen,vol.46:273-284,1895锛�銆侶urwitz鐨勬浠跺悓Routh鐨勬浠跺湪鏈唱(zh矛)涓婃槸涓€鑷寸殑銆俒9]鍥犳閫欎竴绌�(w臎n)瀹氭€у垽鎿�(j霉)鐝�(xi脿n)鍦ㄤ篃琚ū鐐篟outh-Hurwitz绌�(w臎n)瀹氭€у垽鎿�(j霉)[1]銆� 銆€銆€1892骞达紝淇勭緟鏂亯澶х殑鏁�(sh霉)瀛�(xu茅)鍔涘(xu茅)瀹禔.M.Lyapunov锛�1857.5.25-1918.11.3锛夌櫦(f膩)琛ㄤ簡鍏跺叿鏈夋繁閬�(yu菐n)姝峰彶鎰忕京鐨勫崥澹珫鏂団€滈亱(y霉n)鍕�(d貌ng)绌�(w臎n)瀹氭€х殑涓€鑸晱椤屸€濓紙The General Problem of the Stability of Motion,1892锛�銆傚湪閫欎竴璜栨枃涓�锛屼粬鎻愬嚭浜嗙偤鐣�(d膩ng)浠婂(xu茅)琛�(sh霉)鐣屽唬鐐烘噳(y墨ng)鐢ㄤ笖褰遍熆宸ㄥぇ鐨勬潕浜炴櫘璜惧か鏂规硶锛屼篃鍗虫潕浜炴櫘璜惧か绗簩鏂规硶鎴栨潕浜炴櫘璜惧か鐩存帴鏂规硶銆傞€欎竴鏂规硶涓嶅儏鍙敤浜庣窔鎬х郴绲�(t菕ng)鑰屼笖鍙敤浜庨潪绶氭€ф檪(sh铆)璁婄郴绲�(t菕ng)鐨勫垎鏋愯垏瑷�(sh猫)瑷�(j矛)銆傚凡鎴愮偤鐣�(d膩ng)浠婅嚜鍕�(d貌ng)鎺у埗鐞嗚珫瑾茬▼璎涙巿鐨勪富瑕佸収(n猫i)瀹逛箣涓€銆俒11][12] Lyapunov鍦ㄧ┅(w臎n)瀹氭€ф柟闈㈢殑鐮旂┒鍙楀埌Routh鍜孭oincare绛夊伐浣滅殑褰遍熆銆俒12,14] 銆€銆€Lyapunov鏄竴浣嶅ぉ鎵嶇殑鏁�(sh霉)瀛�(xu茅)瀹躲€備粬鏄竴浣嶅ぉ鏂囧(xu茅)瀹剁殑鍏掑瓙銆傛浘寰炲斧浜庡ぇ鏁�(sh霉)瀛�(xu茅)瀹禤.L.Chebyshev锛堣粖姣旀泬澶級锛屽拰A.A.Markov锛堥Μ鐖惧彲澶級鏄悓鏍″悓瀛�(xu茅)锛堟潕姣旈Μ浣庡叐绱�(j铆)锛夛紝骞跺悓浠栧€戝绲備繚鎸佽憲鑹ソ鐨勯棞(gu膩n)绯�銆備粬鍊戝叡鍚屽湪姒傜巼璜栨柟闈㈠仛鍑洪亷鏉板嚭鐨勬垚绺�銆傚湪姒傜巼璜栦腑鎴戝€戝彲浠ョ湅鍒伴棞(gu膩n)浜庣煩鐨勯Μ鐖惧彲澶笉绛夊紡銆佽粖姣旀泬澶笉绛夊紡鍜屾潕浜炴櫘璜惧か涓嶇瓑寮�銆傛潕閭勫湪鐩哥暥(d膩ng)涓€鑸殑姊濅欢涓嬭瓑鏄庝簡涓績妤甸檺瀹氱悊銆俒11][13] 銆€銆€鍜屼粬鐨勭ⅸ澹珫鏂囦竴妯ｏ紝Lyapunov鐨勫崥澹珫鏂囪璀垚娉曟枃骞跺湪Annales de l Universite de Toulouse 锛�1907锛変笂鐧�(f膩)琛�锛�1949骞碢(gu膩n)rinceton University Press閲嶅嵃浜嗘硶鏂囩増銆�1992骞村湪Lyapunov鍗氬＋璜栨枃鐧�(f膩)琛�100鍛ㄥ勾涔嬮殯锛孖NT.J.CONTROL浠ュ皥闆嗗舰寮忕櫦(f膩)琛ㄤ簡Lyapunov璜栨枃鐨勮嫳璀増锛屼互绱€(j矛)蹇典粬鎺у埗鐞嗚珫闋�(l菒ng)鍩熺殑鍗撹秺璨㈢嵒(xi脿n)銆俒11][14] 2.2 璨�(f霉)鍙嶉鏀惧ぇ鍣ㄥ強闋诲煙鐞嗚珫鐨勫缓绔媅15] 銆€銆€鍦ㄦ帶鍒剁郴绲�(t菕ng)绌�(w臎n)瀹氭€х殑浠ｆ暩(sh霉)鐞嗚珫寤虹珛涔嬪悗锛�1928骞达紞1945骞翠互缇庡湅AT&T鍏徃Bell瀵�(sh铆)椹�(y脿n)瀹わ紙Bell Labs锛夌殑绉戝(xu茅)瀹跺€�?y艒u)妤硅?锛屽張寤虹珛浜嗘帶鍒剁郴绲�(t菕ng)鍒嗘瀽鑸囪ō(sh猫)瑷�(j矛)鐨勯牷鍩熸柟娉�銆� 銆€銆€1928骞�8鏈�2鏃ワ紝Harold Black锛�1898-1983锛�锛屽湪鍓嶅線Manhattan瑗胯锛圵est Street锛夌殑涓婄彮閫斾腑锛屽湪Hudson娌崇殑娓¤埞Lackawanna Ferry涓婇潏鍏変竴闁�锛岀櫦(f膩)鏄庝簡鍦ㄧ暥(d膩ng)浠婃帶鍒剁悊璜栦腑鍗犳牳蹇冨湴浣嶇殑璨�(f霉)鍙嶉鏀惧ぇ鍣�銆傜敱浜庢墜闋矑鏈夊悎閬╃殑绱欏嫉锛屼粬灏囧叾鐧�(f膩)鏄庤鍦ㄤ簡涓€浠界磹绱勬檪(sh铆)鍫�(b脿o)锛圱he New York Times锛変笂锛岄€欎唤鏃╁牨(b脿o)宸叉垚鐐轰竴浠剁弽璨寸殑鏂囩墿瑷鸿棌鍦ˋT&T鐨勬獢妗堥え涓€� 銆€銆€鐣�(d膩ng)鏅�(sh铆)鐨凚lack骞村儏29姝�锛屽緸Worcester Polytechnic Institute鐛插緱闆诲瓙宸ョ▼瀛�(xu茅)澹暍妤�(y猫)鍓涘叚骞�銆傛槸瑗块儴闆诲瓙鍏徃宸ョ▼閮紙閫欏€�(g猫)閮ㄥ悗渚嗘垚鐐�1925骞存垚绔嬬殑Bell Labs鐨勬牳蹇冿級鐨勫伐绋嬪斧锛屾鍦ㄥ緸浜嬮浕瀛愮鏀惧ぇ鍣ㄧ殑澶辩湡鍜屼笉绌�(w臎n)瀹氬晱椤岀殑鐮旂┒銆侭lack棣栧厛鎻愬嚭浜嗗熀浜庤宸(b菙)鍎�?sh霉)閭ｆ浼旂朝绗�?锛屽湪姝ゅ熀绀�(ch菙)涓婃渶绲傛彁鍑轰簡璨�(f霉)鍙嶉鏀惧ぇ鍣ㄥ苟灏�(du矛)鍏堕€�(j矛n)琛屼簡鏁�(sh霉)瀛�(xu茅)鍒嗘瀽銆傚悓骞碆lack灏卞叾鐧�(f膩)鏄庡悜?q奴)锛狀崼鐥斿并闅界L閬�(d谩)52闋�126闋�(xi脿ng)鐨勫皥鍒╃敵璜�(q菒ng)锛屼絾鍙埌涔濆勾涔嬪悗锛岀暥(d膩ng)Black鍜屼粬鍦ˋT&T鐨勫悓浜嬪€戦枊鐧�(f膩)鍑哄(sh铆)鐢ㄧ殑璨�(f霉)鍙嶉鏀惧ぇ鍣ㄥ拰璨�(f霉)鍙嶉鐞嗚珫涔嬪悗锛孊lack鎵嶅緱鍒伴€欓爡(xi脿ng)灏堝埄銆� 銆€銆€鍙嶉鏀惧ぇ鍣ㄧ殑鎸暕鍟忛绲﹀叾瀵�(sh铆)鐢ㄥ寲甯朵締浜嗛洠浠ュ厠鏈嶇殑楹荤叐銆傜偤姝arry Nyquist锛�1889-1976锛夊拰鍏朵粬涓€浜汚T&T鐨勯€氳▕宸ョ▼甯粙鍏ヤ簡閫欎竴宸ヤ綔銆侼yquist1917骞村湪鑰堕澶у(xu茅)锛圷ale锛夌嵅鐗╃悊瀛�(xu茅)鍗氬＋瀛�(xu茅)浣�锛屾湁钁楁サ楂樼殑鐞嗚珫閫犺銆�1932骞碞yquist鐧�(f膩)琛ㄤ簡鍖呭惈钁楀悕鐨勨€滀箖濂庢柉鐗瑰垽鎿�(j霉)鈥濓紙Nyquist criterion锛夌殑璜栨枃锛屽苟鍦�1934骞村姞鍏ヤ簡Bell 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Part II,67锛�1948锛�,pp.547-551.鈥濆拰鈥淐ontrol System Synthesis by Root Locus Method, AIEE Trans. Part II,69锛�1950锛�,pp.66-69鈥濆嵆宸插熀鏈笂寤虹珛璧锋牴杌岃贰娉曠殑瀹屾暣鐞嗚珫銆俒18,19锛�27] 銆€銆€Evans鎵€寰炰簨鐨勬槸椋涙(j墨)灏�(d菐o)鑸拰鎺у埗锛屽叾涓秹鍙婅ū澶氬嫊(d貌ng)鎱�(t脿i)绯荤当(t菕ng)鐨勭┅(w臎n)瀹氬晱椤岋紝鍥犳鍏跺凡缍�(j墨ng)鍙堝洖鍒�70澶氬勾鍓峂axwell鍜孯outh鏇惧仛閬庣殑鐗瑰緛鏂圭▼鐨勭爺绌跺伐浣�銆備絾Evans鐢ㄧ郴绲�(t菕ng)鍙冩暩(sh霉)璁婂寲鏅�(sh铆)鐗瑰緛鏂圭▼鐨勬牴璁婂寲杌岃贰渚嗙爺绌�锛岄枊鍓�(chu脿ng)浜嗘柊鐨勬€濈董鍜岀爺绌舵柟娉曘€侲vans鏂规硶涓€鎻愬嚭鍗冲彈鍒颁汉鍊戠殑寤ｆ硾閲嶈锛�1954骞达紝閷㈠(xu茅)妫嵆鍦ㄤ粬鐨勫悕钁椻€滃伐绋嬫帶鍒惰珫鈥濅腑灏堢敤鍏╃瘈(ji茅)浠嬬垂閫欎竴鏂规硶锛屽苟灏囧叾鎴愮偤Evans鏂规硶銆俒8,19] 2.4 鑴堟矕鎺у埗鐞嗚珫鐨勫缓绔嬭垏鐧�(f膩)灞� 銆€銆€闅ㄨ憲瑷�(j矛)绠楁(j墨)鎶€琛�(sh霉)鐨勮獣鐢熷拰鐧�(f膩)灞�锛岃剤娌栨帶鍒剁悊璜栦篃杩呴€熺櫦(f膩)灞曡捣渚嗐€� 銆€銆€鍦ㄩ€欐柟闈㈤鍏堜綔鍑洪噸瑕佽并鐛�(xi脿n)鐨勬槸涔冨鏂壒鍜岄杈�(n贸ng)锛圫hannon锛�銆備箖姘忛鍏堣瓑鏄庢妸姝ｅ鸡淇¤櫉(h脿o)寰炲畠鐨勯噰妯ｅ€煎京(f霉)鐝�(xi脿n)鍑轰締锛屾瘡鍛ㄦ湡鑷冲皯蹇呴爤閫�(j矛n)琛屽叐娆￠噰妯�銆傞杈�(n贸ng)浜�1949骞村畬鍏ㄨВ姹轰簡閫欏€�(g猫)鍟忛銆傞杈�(n贸ng)鐢辨琚垚鐐轰俊鎭珫鐨勫壍(chu脿ng)濮嬩汉銆� 銆€銆€绶氭€ц剤娌栨帶鍒剁悊璜栦互绶氭€у樊鍒嗘柟绋嬬偤鍩虹(ch菙)锛岀窔鎬у樊鍒嗘柟绋嬬悊璜栧湪涓�銆佸洓鍗佸勾浠ｄ腑宸查€愭鐧�(f膩)灞曡捣渚�銆傞毃钁楁媺姘忚畩鎻涘湪寰垎鏂圭▼涓殑鎳�(y墨ng)鐢�锛屽湪宸垎鏂圭▼涓篃闁嬪鍔犱互鎳�(y墨ng)鐢�銆傚埄鐢ㄩ€ｇ簩(x霉)绯荤当(t菕ng)鎷夋皬璁婃彌鍚岄洟鏁ｇ郴绲�(t菕ng)鎷夋皬璁婃彌鐨勫皪(du矛)鎳�(y墨ng)闂�(gu膩n)绯伙紝濂х埦鐧讳集鏍硷紙R.C.Oldenbourg锛夊拰钖╂墭閲屽巹鏂紙H.Sartorious锛変簬1944骞达紝宕旀櫘閲戯紙Tsypkin锛変簬1948骞村垎鍒ユ彁鍑轰簡鑴堟矕绯荤当(t菕ng)鐨勭┅(w臎n)瀹氬垽鎿�(j霉)锛屽嵆绶氭€у樊鍒嗘柟绋嬬殑鎵€鏈夌壒寰佹牴鎳�(y墨ng)浣嶄簬鍠綅鍦撳収(n猫i)銆傜敱浜庨洟鏁ｆ媺姘忚畩鎻涘紡鏄秴瓒婂嚱鏁�(sh霉)锛屽張鎻愬嚭浜嗙敤淇濊璁婃彌灏嘮骞抽潰鐨勫柈浣嶅湏鍏�(n猫i)閮ㄨ綁(zhu菐n)鎻涘埌鏂扮殑骞抽潰鐨勫乏鍗婇潰鐨勬柟娉�锛岄€欐ǎ鍗冲彲浠ヤ娇鐢≧outh-Hurwitz鍒ゆ摎(j霉)锛屽張鍙皣閫ｇ簩(x霉)绯荤当(t菕ng)鍒嗘瀽鐨勯牷鍩熸柟娉曞紩鍏ラ洟鏁ｇ郴绲�(t菕ng)鍒嗘瀽銆� 銆€銆€姹傚緱闆㈡暎鍨嬮牷鐜囩壒鎬у悗锛屼箖姘忕┅(w臎n)瀹氬垽鎿�(j霉)鍜屽叾浠栦竴鍒囩爺绌剁窔鎬х郴绲�(t菕ng)鐨勯牷鐜囨硶閮藉彲鎳�(y墨ng)鐢紝浣嗙敱浜嶣ode鍦栫殑鎳�(y墨ng)鐢ㄥぇ鍙楅檺鍒�锛岄牷鐜囨硶鍦ㄩ洟鏁ｇ郴绲�(t菕ng)鐮旂┒涓篃鍙楀埌闄愬埗銆傦紙搴触锛�1961锛夋浘瑭﹀湒鐢˙ode鍦栦締琛ㄧず闆㈡暎鍨嬮牷鐜囩壒鎬�锛屼絾閬庝簬绻佸京(f霉)鑰岀劇娉曟噳(y墨ng)鐢�銆傦級 銆€銆€鍦ㄨ畩鎻涚悊璜栫殑鐮旂┒鏂归潰锛岄湇鐖剧董鑼诧紙W.Hurewicz锛変簬1947骞撮倎鍑轰簡绗竴姝�锛屼粬棣栧厛寮曢€�(j矛n)浜嗕竴鍊�(g猫)璁婃彌鐢ㄤ簬灏�(du矛)闆㈡暎搴忓垪鐨勮檿鐞嗐€傚湪姝ゅ熀绀�(ch菙)涓�锛屽磾鏅噾浜�1949骞�锛屾媺鏍艰尣灏煎拰鎵庡痉锛圝.R.Ragazzini 鍜� L.A. Zadeh锛変簬1952骞村垎鍒ユ彁鍑轰簡鍜屽畾缇╀簡Z璁婃彌鏂规硶锛屽ぇ澶х啊鍖栦簡閬�(y霉n)绠楁椹�锛屽苟鍦ㄦ鍩虹(ch菙)涓婄櫦(f膩)灞曡捣鑴堟矕鎺у埗绯荤当(t菕ng)鐞嗚珫銆� 銆€銆€鐢变簬Z璁婃彌鍙兘鍙嶆噳(y墨ng)鑴堟矕绯荤当(t菕ng)鍦ㄩ噰妯ｉ粸(di菐n)鐨勯亱(y霉n)鍕�(d貌ng)瑕�(gu墨)寰�锛屽磾鏅噾銆佸反鍏嬬埦锛圧.H.Barker锛夊拰鏈卞埄锛圗.I.Jury锛夊張鍒嗗垾浜�1950骞�銆�1951骞村拰1956骞存彁鍑轰簡寤ｇ京Z璁婃彌鎴栦慨姝璁婃彌锛坢odified Z-transform锛夌殑鏂规硶銆傚皪(du矛)鍚屼竴鍟忛锛屾灄濞佺埦锛圵.K.Linvill锛変篃浜�1951骞寸敤鎻忚堪鍑芥暩(sh霉)鐨勬柟娉曢€�(j矛n)琛屼簡鏈夋晥鐨勭爺绌�锛屼笉閬庨€欎竴鏂规硶鐩墠宸茶純灏戜娇鐢�銆� 銆€銆€鍥為¨鑴堟矕鎺у埗鐞嗚珫鐨勭櫦(f膩)灞曪紝鐩＄淇勫湅鐨勫磾鏅噾鍙婅嫳鍦嬬殑宸村厠鐖剧瓑閮藉仛鍑轰簡涓嶅彲纾ㄦ粎鐨勮并鐛�(xi脿n)锛屼絾寤虹珛鑴堟矕鐞嗚珫鐨勮ū澶氬伐浣滈兘鏄敱缇庡湅鍝ュ€瘮浜炲ぇ瀛�(xu茅)鐨勬媺鏍艰尣灏煎拰浠栫殑鍗氬＋鐢熷€戝畬鎴愮殑銆備粬鍊戝寘鎷湵閲岋紙闆㈡暎绯荤当(t菕ng)绌�(w臎n)瀹氱殑鏈遍噷鍒ゅ叿锛岃兘瑙€娓€ц垏鑳介仈(d谩)鎬�锛屽垎鏋愯垏瑷�(sh猫)瑷�(j矛)宸ュ叿绛夛級锛屽崱鐖炬浖锛堥洟鏁ｇ媭鎱�(t脿i)鏂规硶锛岃兘鎺ф€ц垏鑳借鎬х瓑銆傛槸鑷帶鐣岀浜屼綅鐛睮EEE Model of Honor鑰咃紙1974锛夛級锛屾墡寰凤紙Z璁婃彌瀹氱京绛夈€傛槸鑷帶鐣岀浜斾綅鐛睮EEE Model of Honor鑰咃紙1995锛夛級銆備簲鍗佸勾浠ｆ湯锛岃剤娌栫郴绲�(t菕ng)鐨刏璁婃彌娉曞凡鑷绘垚鐔�锛屽ソ骞炬湰鏁欑鏇稿悓鏅�(sh铆)鍑虹増銆俒16,17] 2.5 姝峰彶涓婄殑涓夋湰閲嶈钁椾綔[27] 鍦ㄦ帶鍒剁悊璜栫櫦(f膩)灞曠殑姝峰彶涓婃湁涓夐儴钁椾綔鐗瑰垾鍊煎緱涓€鎻�锛屽嵆 鐩墠琚綔鐐轰俊鎭珫闁嬬鐨勯杈�(n贸ng)锛圕laude Elwood Shannon,1916-锛夌殑璜栨枃锛� 銆婇€氳▕鐨勬暩(sh霉)瀛�(xu茅)鐞嗚珫銆嬶紙A Mathematical Theory of Communication锛� 銆€銆€1948骞寸櫦(f膩)琛ㄥ湪銆婅矟鐖剧郴绲�(t菕ng)鎶€琛�(sh霉)闆滃織銆嬬27鍗枫€傞€欑瘒璜栨枃鍚屽叾1949骞寸櫦(f膩)琛ㄧ殑璜栨枃銆婂櫔鑱蹭腑鐨勯€氳▕銆嬶紙Communication in Presence of Noise.Proc.IRE,37,10-21锛夊瀹氫簡淇℃伅璜栫殑鍩虹(ch菙)銆� 鎺у埗璜栧壍(chu脿ng)绔嬭€呯董绱嶏紙Norbert Wienner,1894-1964锛夌殑缍�(j墨ng)鍏歌珫钁楋細 銆€銆€銆婃帶鍒惰珫锛屾垨闂�(gu膩n)浜庡湪鍕�(d貌ng)鐗╁拰姗�(j墨)鍣ㄤ腑鎺у埗鍜岄€氳▕鐨勭瀛�(xu茅)銆嬶紙Cybernetics or Control and Communication in the annimal and the machines. 1948锛� 銆€銆€閷㈠(xu茅)妫紙Tsien H S,1991-锛夌殑钁椾綔 銆€銆€銆婂伐绋嬫帶鍒惰珫銆嬶紙Engineering Cybernetics. 1954锛� 銆€銆€閫欎笁閮ㄨ憲浣滃皪(du矛)浜洪绀炬渻(hu矛)鏈夎憲宸ㄥぇ鐨勫奖闊�锛岀敘(ch菐n)鐢熶簡鏂板瀷鐨勭稖鍚堟€у熀绀�(ch菙)鐞嗚珫锛氭帶鍒惰珫锛屼俊鎭珫鍜屽伐绋嬫帶鍒惰珫銆� 銆€銆€鍦ㄤ腑鍦�锛�1954骞村嚭鐗堜簡鐢卞妷璞圭法瀵殑绗竴鏈€婅嚜鍕�(d貌ng)鎺у埗鍘熺悊銆嬪皥钁楋紙涓婃捣锛氫腑鍦嬬瀛�(xu茅)鍦栨浉鍎€鍣ㄥ叕鍙�.1954锛夈€� 3. 姝峰彶鐨勬€濊€� 銆€銆€鍥為¨鎺у埗鎶€琛�(sh霉)鍜屾帶鍒剁悊璜栧咕鍗冨勾鐨勭櫦(f膩)灞曟鍙�锛屾垜鍊戝彲浠ョ附绲�(ji茅)鍑虹瀛�(xu茅)鐧�(f膩)灞曠殑骞惧€�(g猫)鐗归粸(di菐n)锛� 1锛夌ぞ鏈�(hu矛)鐧�(f膩)灞曠殑闇€瑕佹槸绉戝(xu茅)鐧�(f膩)灞曠殑鍕�(d貌ng)鍔�銆� 銆€銆€鎺у埗鎶€琛�(sh霉)鐨勫瓨鍦ㄨ垏鐧�(f膩)灞曞凡鏈夋暩(sh霉)鍗冨勾鐨勬鍙�锛屼絾鍙湁鍦ㄥ伐妤�(y猫)鐨勭櫦(f膩)灞曞皪(du矛)鍕�(d貌ng)鍔涚敘(ch菐n)鐢熷法澶х殑闇€姹�锛岃捀姘ｆ(j墨)绌�(w臎n)瀹氭€у晱椤屽嚭鐝�(xi脿n)骞跺叿鏈夎嚦闂�(gu膩n)閲嶈鐨勬剰缇╂檪(sh铆)锛屼汉鍊戞墠闆嗕腑鏅哄姏渚嗚В姹洪€欎竴闆ｉ锛屽苟鐢辨鐢�(ch菐n)鐢熶簡绌�(w臎n)瀹氭€х悊璜栥€傞牷鍩熸柟娉曞拰闆㈡暎锛堣剤娌栵級绯荤当(t菕ng)鐞嗚珫鍚屾ǎ濡傛锛屼篃鏄湪閫氳▕鎶€琛�(sh霉)鍜岃▓(j矛)绠楁(j墨)鎶€琛�(sh霉)鐨勭櫦(f膩)灞曢亷绋嬩腑鐐鸿В姹洪棞(gu膩n)閸靛晱椤岃€岀櫦(f膩)灞曡捣渚嗙殑銆� 銆€銆€閷笁寮�(qi谩ng)鍏堢敓灏辨浘鎸囧嚭锛氣€滅瀛�(xu茅)渚嗘簮浜庣敓鐢�(ch菐n)鍜屽皪(du矛)鑷劧鐝�(xi脿n)璞＄殑瑙€瀵�锛屽畠鐨勭櫦(f膩)灞曞彇姹轰簬鐢熺敘(ch菐n)鍜岀ぞ鏈�(hu矛)鐨勯渶姹�?锛佺浀20] 2锛夌瀛�(xu茅)鐨勯€�(j矛n)姝ユ槸闆嗛珨鍔姏鐨勭祼(ji茅)鏋�锛屽湪閫欎竴榛�(di菐n)涓婂線寰€椤ず鍑虹瀛�(xu茅)瀹剁殑缇ら珨鏁堟噳(y墨ng)銆� 銆€銆€鍚屾棭鏈熺瀛�(xu茅)鐞嗚珫鐨勭櫦(f膩)灞曚笉鍚岋紝鐝�(xi脿n)浠ｉ珮鏂版妧琛�(sh霉)鐨勭櫦(f膩)灞曡渚濊炒浜庨泦楂旂殑鏅烘収銆傜┅(w臎n)瀹氭€х悊璜栥€侀牷鍩熺悊璜栧強鑴堟矕鐞嗚珫鐨勫缓绔嬭垏鐧�(f膩)灞曞緢濂藉湴瑾槑浜嗛€欎竴榛�(di菐n)銆� 3锛夌瀛�(xu茅)鐨勭櫦(f膩)鏄庤垏绉戝(xu茅)鐞嗚珫鐨勫缓绔嬫湁璩翠簬绉戝(xu茅)瀹跺爡(ji膩n)瀵�(sh铆)鐨勭煡璀�(sh铆)鍩虹(ch菙)銆傛澃鍑虹殑绉戝(xu茅)瀹跺ぇ澶氭槸澶氶潰鐧�(f膩)灞曠殑銆� 銆€銆€瑕佺従(xi脿n)浠ｇ瀛�(xu茅)鐞嗚珫鐨勫缓绔嬫湁璩翠簬鏈夊爡(ji膩n)瀵�(sh铆)鑸囨繁鍘氱殑鐭ヨ瓨(sh铆)鍩虹(ch菙)銆侭lack闆栫劧鏈€鏃╂彁鍑轰簡璨�(f霉)鍙嶉鏀惧ぇ鍣ㄧ殑鎬濇兂锛屼絾鐢变簬浠栨湰浜虹悊璜栧熀绀�(ch菙)杓冨樊锛堝(xu茅)澹(xu茅)浣�锛屽彧鏈夊叚銆佷竷骞寸殑宸ヤ綔缍�(j墨ng)椹�(y脿n)锛�锛岄牷鍩熺悊璜栧嵒鏄湪Nyquist鍗氬＋鍜孊ode鍗氬＋绛夌殑鍔姏涓嬪缓绔嬬殑銆侭lack鏈汉鐨勮珫鏂囦篃鏄湪鍙冭€冧簡Nyquist鐨勮珫鏂囦箣鍚庢墠瀹屾垚锛屼粬鐨勫皥鍒╃敵璜�(q菒ng)涔熸槸鍦∟yquist绛夌殑宸ヤ綔瀹屾垚鍚庢墠琚獚(r猫n)鍙苟鐛叉簴(zh菙n)鐨�銆傚悓妯�锛屽湪鎺у埗鐞嗚珫鐧�(f膩)灞曞彶涓婂仛鍑哄法澶ц并鐛�(xi脿n)鐨勭瀛�(xu茅)瀹跺Maxwell銆丩yapunov銆乑adeh銆丣uly绛夌劇涓嶅湪澶氬€�(g猫)鏂归潰鍧囨湁寤烘ü銆� 4锛夋矑鏈夌悊璜�锛岀ぞ鏈�(hu矛)瀵�(sh铆)韪愬氨涓嶈兘鎴愮偤绯荤当(t菕ng)鐨勭瀛�(xu茅)锛屽(sh铆)韪愪篃灏遍洠浠ユ繁鍏ュ拰绯荤当(t菕ng)鍦扮櫦(f膩)灞�銆� 銆€銆€鎺у埗鎶€琛�(sh霉)鍜岀悊璜栫殑鐧�(f膩)灞曢倓琛ㄦ槑浜嗛€欐ǎ涓€鍊�(g猫)閬撶悊锛氫换浣曠ぞ鏈�(hu矛)瀵�(sh铆)韪愭矑鏈夌悊璜栧氨涓嶈兘鎴愮偤绉戝(xu茅)锛屼篃灏遍洠浠ョ櫦(f膩)灞�?锛熷垈钀嶅すg(sh霉)鍦ㄤ腑鍦嬪拰宸存瘮鍊凡鏈夋暩(sh霉)鍗冨勾鐨勬鍙�锛屼絾鐢变簬娌掓湁涓婂崌鐐虹悊璜�锛屽彧鑳藉湪浣庣礆(j铆)鐨勬按骞充笂鐧�(f膩)灞曘€�1868骞翠互渚�锛岄毃钁楁帶鍒剁悊璜栫殑寤虹珛锛屾帶鍒剁悊璜栧拰鎺у埗鎶€琛�(sh霉)鍚屾檪(sh铆)闁嬪椋涢€熺櫦(f膩)灞�锛屾帶鍒舵妧琛�(sh霉)绲備簬鎴愮偤浜哄€戝緛鏈嶈嚜鐒惰垏鏀归€犺嚜鐒剁殑鏈夊姏姝﹀櫒銆備笉鍍呬簬姝�锛岀敱浜庢垜鍊戜腑鍦嬪咕鍗冨勾渚嗗彧閲嶆妧琛�(sh霉)涓嶉噸鐞嗚珫锛屾垜鍊戠従(xi脿n)鍦ㄧ殑姝峰彶灏辨槸鍗佸叚銆佸崄涓冧笘绱€(j矛)鍓嶁€滅嚘鐖涜紳鐓岀殑鍙や唬鏂囨槑鈥�锛岃€屽湪鍗佸叚銆佸崄涓冧笘绱€(j矛)瑗挎柟绉戝(xu茅)鐞嗚珫楂旂郴闁嬪寤虹珛涔嬪悗锛屽氨闁嬪鐩稿皪(du矛)鏃ヨ定鏈惤锛岀祩浜庡埌浜嗏€滆惤鍚庘€濈殑杩戜唬锛屾尐鎵撳彈娆�锛屼互鑷充簬鈥滃柂娆�(qu谩n)杈卞湅鈥濅簡銆� 锛�1998/5/5淇敼,鍘熸枃鐧�(f膩)琛ㄤ簬銆婅嚜鍕�(d貌ng)鍖栧崥瑕姐€�1996骞寸5鏈�22-25锛� 鍙冭€冩枃鐛�(xi脿n) [1][鑻盷鏉庣磩鐟�. 涓湅绉戝(xu茅)鎶€琛�(sh霉)鍙�. 绗洓鍗峰ぉ瀛�(xu茅)绗簩鍒嗗唺(c猫). 鍖椾含: 绉戝(xu茅)鍑虹増绀�,336-341,1975 [2]鍚屼笂,340-377. 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