LMIs in Control Systems: Analysis, Design and Applications

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