| Preface | p. v |
| Systems and Control | p. 1 |
| Notation | p. 1 |
| State space description | p. 3 |
| Transfer functions | p. 6 |
| Proper rational functions | p. 7 |
| Power series expansions | p. 9 |
| State space realizations of transfer functions | p. 13 |
| Notes | p. 17 |
| Stability | p. 19 |
| State space stability | p. 19 |
| Mechanical systems | p. 20 |
| Input-output stability | p. 23 |
| The H[superscript infinity] norm | p. 25 |
| Notes | p. 27 |
| Lyapunov Theory | p. 29 |
| Basic Lyapunov theory | p. 29 |
| Lyapunov functions | p. 33 |
| Lyapunov functions and related bounds | p. 34 |
| Bounds on e[superscript At] | p. 34 |
| Some system bounds | p. 36 |
| Lyapunov functions for mechanical systems | p. 38 |
| Notes | p. 39 |
| Observability | p. 41 |
| Observability | p. 41 |
| Unobservable eigenvalues and the PBH test | p. 45 |
| An observability least squares problem | p. 46 |
| Stability and observability | p. 50 |
| Notes | p. 53 |
| Controllability | p. 55 |
| Controllability | p. 55 |
| Uncontrollable eigenvalues and the PBH test | p. 58 |
| A controllability least squares problem | p. 59 |
| Stability and controllability | p. 61 |
| Notes | p. 64 |
| Controllable and Observable Realizations | p. 67 |
| Invariant subspaces | p. 67 |
| The controllable and observable decomposition | p. 69 |
| A minimal realization procedure | p. 75 |
| The minimal polynomial and realizations | p. 77 |
| The inverse of a transfer function | p. 80 |
| Notes | p. 82 |
| More Realization Theory | p. 83 |
| The restricted backward shift realization | p. 83 |
| System Hankel operators | p. 89 |
| Realizations and factoring Hankel matrices | p. 91 |
| Partial realizations and the Kalman-Ho Algorithm | p. 96 |
| The Kalman-Ho Algorithm | p. 102 |
| Matrix representation of operators | p. 102 |
| Shift realizations for proper rational functions | p. 106 |
| Jordan form realizations | p. 113 |
| Notes | p. 116 |
| State Feedback and Stabilizability | p. 119 |
| State feedback and stabilizability | p. 119 |
| Simple stabilizing controllers | p. 120 |
| Stabilizability and uncontrollable eigenvalues | p. 122 |
| Eigenvalue placement | p. 123 |
| An eigenvalue placement procedure | p. 123 |
| Ackermann's Formula | p. 125 |
| Controllable canonical form | p. 126 |
| Transformation to controllable canonical form | p. 128 |
| Eigenvalue placement by state feedback | p. 130 |
| Multivariable eigenvalue placement | p. 130 |
| Two canonical forms | p. 135 |
| Transfer functions and feedback | p. 141 |
| Notes | p. 143 |
| State Estimators and Detectability | p. 145 |
| Detectability | p. 145 |
| State estimators | p. 148 |
| Eigenvalue placement for estimation error | p. 149 |
| Notes | p. 151 |
| Output Feedback Controllers | p. 153 |
| Static output feedback | p. 153 |
| Transfer function considerations | p. 154 |
| Dynamic output feedback | p. 156 |
| Observer based controllers | p. 158 |
| Notes | p. 162 |
| Zeros of Transfer Functions | p. 163 |
| Zeros | p. 163 |
| The system matrix | p. 165 |
| Notes | p. 170 |
| Linear Quadratic Regulators | p. 171 |
| The finite horizon problem | p. 171 |
| Problems with control weights | p. 174 |
| An operator approach | p. 175 |
| An operator based solution | p. 175 |
| The adjoint system | p. 177 |
| The Riccati equation | p. 179 |
| An operator quadratic regulator problem | p. 180 |
| A linear quadratic tracking problem | p. 182 |
| A spectral factorization | p. 184 |
| A general tracking problem | p. 186 |
| The infinite horizon problem | p. 189 |
| The algebraic Riccati equation | p. 190 |
| Solution to the infinite horizon problem | p. 193 |
| Problems with control weights | p. 195 |
| An outer spectral factorization | p. 196 |
| The root locus and the quadratic regulator | p. 198 |
| Some comments on the outer spectral factor | p. 202 |
| Notes | p. 204 |
| The Hamiltonian Matrix and Riccati Equations | p. 205 |
| The Hamiltonian matrix and stabilizing solutions | p. 205 |
| Computation of the stabilizing solution | p. 210 |
| Characteristic polynomial of the Hamiltonian matrix | p. 211 |
| Some special cases | p. 212 |
| The linear quadratic regulator | p. 214 |
| H[superscript infinity] analysis and control | p. 216 |
| The Riccati differential equation | p. 219 |
| A two point boundary value problem | p. 219 |
| Some properties | p. 221 |
| Notes | p. 224 |
| H[superscript infinity] Analysis | p. 227 |
| A disturbance attenuation problem | p. 227 |
| A Riccati equation | p. 229 |
| An abstract optimization problem | p. 234 |
| An operator disturbance attenuation problem | p. 235 |
| The disturbance attenuation problem revisited | p. 236 |
| The adjoint system | p. 237 |
| The Riccati equation | p. 239 |
| A spectral factorization | p. 241 |
| A general disturbance attenuation problem | p. 242 |
| The infinite horizon problem | p. 244 |
| Stabilizing solutions to the algebraic Riccati equation | p. 247 |
| An outer spectral factor | p. 249 |
| The root locus and the H[superscript infinity] norm | p. 250 |
| Notes | p. 254 |
| H[superscript infinity] Control | p. 255 |
| A H[superscript infinity] control problem | p. 255 |
| Problem solution | p. 256 |
| The central controller | p. 261 |
| Some abstract max-min problems | p. 263 |
| The Riccati differential equation and norms | p. 268 |
| The infimal achievable gain | p. 270 |
| A two point boundary value problem | p. 271 |
| The Riccati differential equation | p. 273 |
| The infinite horizon problem | p. 274 |
| The stabilizing solution | p. 277 |
| The scalar valued case | p. 281 |
| The central controller | p. 282 |
| An operator perspective | p. 284 |
| A tradeoff between norms | p. 288 |
| The L[superscript 2] norm of an operator | p. 288 |
| The L[superscript 2] norm of a system | p. 289 |
| The L[superscript 2] optimal cost | p. 291 |
| A tradeoff between d[subscript infinity] and d[subscript 2] | p. 293 |
| A tradeoff between the H[superscript 2] and H[superscript infinity] norms | p. 295 |
| Notes | p. 297 |
| Appendix: Least Squares | p. 299 |
| The Projection Theorem | p. 299 |
| A general least squares optimization problem | p. 302 |
| Computation of orthogonal projections | p. 305 |
| The Gram matrix | p. 309 |
| An application to curve fitting | p. 312 |
| Minimum norm problems | p. 313 |
| The singular value decomposition | p. 317 |
| Schmidt pairs | p. 319 |
| A control example | p. 323 |
| State space | p. 324 |
| The L[superscript 2]-L[superscript infinity] gain | p. 325 |
| Notes | p. 327 |
| Bibliography | p. 329 |
| Index | p. 337 |
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