LMIs in control systems : analysis, design and applications /: analysis, design and applications. (2013)

• Record Type: Book
• Further Information: Note: By Guang-Ren Duan.
• Authors: Duan, Guangren
• Contents: Introduction; What are LMIs?; General form Standard form; Manipulations; A few examples involving LMIs Eigenvalue minimization Matrix norm minimization A key step in μ -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<BR&g
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2013
• Extent: 1 online resource (483 pages), (29 illustrations)
• Subjects: 629.8; Control theory; Matrix inequalities; Mathematical optimization
• Languages: English
• ISBNs: 9781466583009; 1466583002
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.