# Linear Systems Theory

Princeton University Press, Aug 24, 2009 - Mathematics - 280 pages

Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. In this textbook, Joćo Hespanha covers the key topics of the field in a unique lecture-style format, making the book easy to use for instructors and students. He looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization, and examines advanced foundational topics such as multivariable poles and zeros, and LQG/LQR.

The textbook presents only the most essential mathematical derivations, and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these important tools. The balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Solutions to the theoretical and computational exercises are also available for instructors.

• Easy-to-use textbook in unique lecture-style format
• Sidebars explain topics in further detail
• Annotated proofs and discussions of MATLAB commands
• Balanced chapters can each be taught in two hours of course lecture
• Solutions to exercises available to instructors

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### Contents

 IV 5 VII 7 VIII 10 IX 11 XIII 14 XIV 15 XV 19 XVI 22
 CXXXV 133 CXXXVI 135 CXXXIX 136 CXLI 137 CXLII 138 CXLIII 139 CXLIV 140 CXLV 141

 XX 24 XXI 25 XXII 27 XXV 28 XXVI 29 XXVII 30 XXVIII 31 XXXII 32 XXXIV 36 XXXV 38 XXXVI 39 XXXVII 41 XL 43 XLI 44 XLIII 45 XLIV 46 XLVII 47 XLVIII 49 XLIX 50 LII 51 LIII 53 LIV 55 LVII 57 LVIII 58 LIX 59 LX 60 LXI 61 LXII 63 LXV 65 LXVI 66 LXVII 67 LXX 70 LXXII 72 LXXIV 77 LXXV 78 LXXVI 80 LXXX 81 LXXXI 84 LXXXII 85 LXXXIV 86 LXXXV 87 LXXXVIII 88 LXXXIX 89 XC 91 XCII 93 XCIII 95 XCVI 96 XCVII 99 XCIX 100 C 101 CI 102 CII 105 CIII 109 CV 110 CIX 111 CX 113 CXI 116 CXIII 117 CXIV 118 CXVIII 119 CXX 120 CXXI 121 CXXII 122 CXXIV 123 CXXVII 124 CXXVIII 125 CXXIX 126 CXXXI 127 CXXXII 128 CXXXIII 129
 CXLVI 142 CXLVII 144 CXLIX 145 CLI 148 CLV 152 CLVII 153 CLVIII 154 CLIX 155 CLXI 156 CLXIII 157 CLXVII 158 CLXVIII 160 CLXIX 161 CLXX 163 CLXXII 165 CLXXIII 167 CLXXIV 169 CLXXVIII 170 CLXXIX 172 CLXXX 173 CLXXXI 175 CLXXXIII 176 CLXXXV 177 CXC 178 CXCII 180 CXCIV 182 CXCV 183 CXCVII 184 CXCVIII 185 CC 186 CCI 187 CCII 189 CCIII 191 CCVI 192 CCVII 193 CCIX 194 CCX 195 CCXII 196 CCXIV 197 CCXVII 198 CCXVIII 199 CCXX 203 CCXXI 204 CCXXV 205 CCXXVI 207 CCXXVII 210 CCXXVIII 213 CCXXIX 216 CCXXXI 217 CCXXXII 222 CCXXXIII 223 CCXXXVI 228 CCXXXVII 229 CCXXXVIII 230 CCXL 231 CCXLII 235 CCXLIV 236 CCXLV 238 CCXLVII 239 CCXLVIII 241 CCXLIX 242 CCL 243 CCLIII 246 CCLVI 248 CCLVII 253 CCLVIII 255 CCLIX 257 CCLX 259 Copyright