LMIs in control systems : analysis, design and applications

Content: Introduction What are LMIs?      General form       Standard form      Manipulations  A few examples involving LMIs       Eigenvalue minimization       Matrix norm minimization       A key step in mu-analysis       Schur stabilization  A brief history      The seed planted (1890)      The rooting period (1940-1970)       The growing period (1970-2000)       The Nourishing period (2000-present) Advantages  About the book       Structure       Features       Using it in courses  Exercises  PRELIMINARIES   Technical Lemmas Generalized square inequalities      The restriction-free inequality       Inequalities with restriction      The variable elimination lemma Schur complement lemma      Schur complements       Matrix inversion lemma       Schur complement lemma  Elimination of variables       Variable elimination in a partitioned matrix      The projection lemma       The reciprocal projection lemma  Some other useful results       Trace of an LMI       The maximum modulus principle       The Parseval lemma  Notes and references  Exercises   Review of Optimization Theory  Convex sets       Definitions and properties      Hyperplanes, halfspaces, polyhedrons and polytopes  Convex functions       Definition and properties      Criteria Mathematical optimization       Least squares programming      Linear programming      Quadratic programming  Convex optimization       The problem       Local and global optima  The LMI problem      Convexity      The extreme result       Standard problems  Notes and references      About this chapter       The open source software CVX      A counter example for numerical reliability Exercises   CONTROL SYSTEMS ANALYSIS   Stability Analysis  Hurwitz and Schur stability       Hurwitz stability       Schur stability D-stability       Special cases       GeneralLMI regions       Generalized Lyapunov theorem  Quadratic stability       Familyof systems      Quadratic Hurwitz stability       QuadraticSchur stability  Quadratic D-stability       Definition and main results       Some special cases Time-delay systems       The delay independent condition      The delay dependent condition  Notes and references       Summary and references       Affine quadratic stability  Exercises   H /H2 Performance  H  and H2 indices       H  index       H2 index      Equivalent definitions  LMI conditions for H  index       Thebasic conditions       Deduced conditions  LMI conditions for H2 index      Basic conditions       Deduced conditions Notes and references  Exercises   Property Analysis  Hurwitz stabilizability and detectability       Hurwitz stabilizability       Hurwitz detectability  Schur stabilizability and detectability       Schur stabilizability       Schur detectability  Dissipativity       Definition       Equivalent conditions  Passivity and positive-realness       Definitions       The positive-real lemma      The LMI condition  Non expansivity and bounded-realness       Definitions       The bounded-real lemma       The LMI conditions  Notes and references  Exercises   CONTROL SYSTEMS DESIGN  Feedback Stabilization  State feedback stabilization      Case of continuous-time systems      Case of discrete-time systems  D-stabilization       H (a,B)-stabilization       D(q,r)-stabilization      General D-stabilization  Quadratic stabilization       Family of systems      Quadratic Hurwitz stabilization       Quadratic Schur stabilization  Quadratic D-stabilization      Problem formulation       The solution       Special cases Insensitive region design       Sensitivity of matrix eigen values       Insensitive strip region design       Insensitive disk region design  Robust stabilization of second-order systems       Stabilization       Robust Stabilization  Stabilization of time-delay systems       Case of delay independence       Case of delay dependence  Notes and references  Exercises         H /H2 Control H  state feedback control      The problem       The solution       Other conditions  H2 state feedback control      The problem       The solution       Other conditions  Robust H /H2 state feedback control       The problems      Solution to the robust H  control problem       Solution to the robust H2 control problem  LQ regulation via H2 control       Problem description       Relation with H2 performance      The solution  Notes and references       Summary and references      Dissipative, passive, and non-expansive control  Exercises   State Observation and Filtering  Full- and reduced-order state observers        Full-order state observers       Reduced-order state observer design  Full-order H /H2 state observers       Problems formulation       Solutions to problems       Examples  H  filtering       Problems formulation       Solution to H  filtering  H2 filtering      Problems formulation       Solution to H2 filtering  Notes and references  Exercises      Multiple Objective Designs Insensitive region designs with minimum gains       Insensitive strip region designs with minimum gains       Insensitive disk region designs with minimum gains  Mixed H /H2 designs with desired LMI pole regions       The problem       Solutions to the problem  Mixed robust H /H2 designs with desired LMI pole regions       The problem       Solutions to the problem  Notes and references       Summary of main results      Further remarks Exercises   APPLICATIONS   Missile Attitude Control  The dynamical model      Models for non-rotating missiles       Models for BTT missiles  Attitude control of non-rotating missiles       The problem       The solution  Attitude control of BTT missiles       The problem       Quadratic stabilization       Numerical results and simulation Notes and references  Exercises   Satellite Control  System modelling       The second-order system form       The state space form  H2 and H  feedback control       H  control       H2 control  Mixed H2/ H  feedback control       The problem       Numerical and simulation results  Notes and references  Exercises   APPENDICES  Proofs of Theorems   Proof of Theorem 4.1       Preliminaries       Sufficiency       Necessity   Proof of Theorem 5.1       The first step       The second step  Proof of Theorem5.2      The first step      The second step