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1 | (31) |
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Linear Time-Invariant Systems |
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1 | (2) |
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3 | (2) |
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5 | (1) |
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First-Order Autonomous Nonlinear Systems |
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5 | (3) |
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Second-Order Systems: Phase-Plane Analysis |
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8 | (2) |
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Phase-Plane Analysis of Linear Time-Invariant Systems |
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10 | (8) |
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Phase-Plane Analysis of Nonlinear Systems |
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18 | (2) |
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18 | (2) |
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20 | (2) |
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21 | (1) |
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Examples of Nonlinear Systems |
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22 | (5) |
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Magnetic Suspension System |
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23 | (2) |
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Inverted Pendulum on a Cart |
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25 | (1) |
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26 | (1) |
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27 | (4) |
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Mathematical Preliminaries |
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31 | (34) |
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31 | (1) |
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32 | (1) |
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32 | (7) |
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Linear Independence and Basis |
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34 | (2) |
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36 | (1) |
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37 | (2) |
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39 | (5) |
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Eigenvalues, Eigenvectors, and Diagonal Forms |
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40 | (1) |
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41 | (3) |
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44 | (1) |
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44 | (1) |
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45 | (1) |
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46 | (3) |
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Bounded Linear Operators and Matrix Norms |
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48 | (1) |
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49 | (3) |
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51 | (1) |
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52 | (2) |
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54 | (2) |
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Solution of Differential Equations |
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56 | (3) |
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59 | (6) |
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Lyapunov Stability I: Autonomous Systems |
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65 | (42) |
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65 | (4) |
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Positive Definite Functions |
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69 | (2) |
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71 | (3) |
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74 | (3) |
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Asymptotic Stability in the Large |
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77 | (3) |
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Positive Definite Functions Revisited |
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80 | (2) |
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82 | (1) |
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Construction of Lyapunov Functions |
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82 | (3) |
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85 | (8) |
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93 | (3) |
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Analysis of Linear Time-Invariant Systems |
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96 | (4) |
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Linearization of Nonlinear Systems |
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99 | (1) |
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100 | (2) |
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102 | (5) |
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Lyapunov Stability II: Nonautonomous Systems |
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107 | (30) |
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107 | (3) |
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Positive Definite Functions |
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110 | (3) |
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111 | (2) |
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113 | (2) |
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Proof of the Stability Theorems |
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115 | (4) |
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Analysis of Linear Time-Varying Systems |
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119 | (3) |
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The Linearization Principle |
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120 | (2) |
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122 | (3) |
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125 | (1) |
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126 | (1) |
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127 | (3) |
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Stability of Discrete-Time Systems |
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130 | (3) |
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130 | (1) |
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Discrete-Time Positive Definite Functions |
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131 | (1) |
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132 | (1) |
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133 | (4) |
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137 | (18) |
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Basic Feedback Stabilization |
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138 | (3) |
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141 | (4) |
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Backstepping: More General Cases |
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145 | (6) |
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145 | (3) |
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148 | (3) |
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151 | (2) |
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153 | (2) |
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155 | (28) |
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156 | (3) |
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157 | (2) |
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159 | (5) |
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Linear Time-Invariant Systems |
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164 | (2) |
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166 | (2) |
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166 | (1) |
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167 | (1) |
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Closed-Loop Input--Output Stability |
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168 | (3) |
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171 | (3) |
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174 | (4) |
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178 | (2) |
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180 | (3) |
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183 | (18) |
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183 | (2) |
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185 | (1) |
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Input-to-State Stability (ISS) Theorems |
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186 | (5) |
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189 | (2) |
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Input-to-State Stability Revisited |
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191 | (4) |
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Cascade-Connected Systems |
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195 | (3) |
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198 | (3) |
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201 | (22) |
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Power and Energy: Passive Systems |
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201 | (3) |
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204 | (4) |
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Interconnections of Passivity Systems |
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208 | (3) |
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210 | (1) |
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Stability of Feedback Interconnections |
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211 | (3) |
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Passivity of Linear Time-Invariant Systems |
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214 | (3) |
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Strictly Positive Real Rational Functions |
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217 | (3) |
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220 | (3) |
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223 | (32) |
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224 | (1) |
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Differentiable Storage Functions |
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225 | (1) |
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Back to Input-to-State Stability |
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226 | (1) |
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226 | (3) |
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229 | (2) |
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Mass-Spring System with Friction |
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229 | (2) |
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Mass--Spring System without Friction |
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231 | (1) |
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231 | (2) |
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Algebraic Condition for Dissipativity |
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233 | (4) |
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235 | (2) |
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Stability of Dissipative Systems |
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237 | (2) |
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Feedback Interconnections |
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239 | (4) |
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243 | (4) |
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Linear Time-Invariant Systems |
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245 | (1) |
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Strictly Output Passive Systems |
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246 | (1) |
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Some Remarks about Control Design |
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247 | (4) |
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Nonlinear L2-Gain Control |
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251 | (2) |
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253 | (2) |
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255 | (36) |
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255 | (10) |
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256 | (1) |
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257 | (2) |
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259 | (1) |
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Coordinate Transformations |
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259 | (2) |
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261 | (4) |
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Input--State Linearization |
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265 | (5) |
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Systems of the Form x = Ax + Bω(x)[u -- φ(x)] |
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265 | (2) |
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Systems of the Form x = f(x) + g(x)u |
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267 | (3) |
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270 | (3) |
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Conditions for Input--State Linearization |
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273 | (2) |
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Input--Output Linearization |
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275 | (5) |
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280 | (7) |
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Conditions for Input--Output Linearization |
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287 | (1) |
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287 | (4) |
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291 | (16) |
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Observers for Linear Time-Invariant Systems |
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291 | (5) |
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292 | (2) |
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294 | (1) |
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Observers for Linear Time-Invariant Systems |
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294 | (1) |
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295 | (1) |
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296 | (2) |
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298 | (1) |
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Observers with Linear Error Dynamics |
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298 | (3) |
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301 | (2) |
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Nonlinear Separation Principle |
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303 | (4) |
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307 | (30) |
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307 | (6) |
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313 | (2) |
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315 | (5) |
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320 | (4) |
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324 | (4) |
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328 | (2) |
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330 | (7) |
| Bibliography |
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337 | (8) |
| List of Figures |
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345 | (4) |
| Index |
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349 | |