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By Guang-Ren Duan, Hai-Hua Yu
"Preface lately linear matrix inequalities (LMIs) have emerged as a strong device within the box of keep an eye on platforms research and layout. Many difficulties reminiscent of country suggestions synthesis, robustness research and layout, H2 and H? regulate, can all be lowered to convex or quasi-convex difficulties that contain LMIs. the main beautiful characteristic of LMIs lies within the indisputable fact that many difficulties in platforms and keep an eye on can be Read more...
summary: "Preface in recent times linear matrix inequalities (LMIs) have emerged as a robust device within the box of keep an eye on platforms research and layout. Many difficulties comparable to kingdom suggestions synthesis, robustness research and layout, H2 and H? regulate, can all be decreased to convex or quasi-convex difficulties that contain LMIs. the main beautiful function of LMIs lies within the undeniable fact that many difficulties in structures and keep watch over might be decreased to LMI difficulties, which might be solved either successfully and numerical reliably. Very effective algorithms to unravel linear matrix inequalities were constructed and will be without problems used during the mature Matlab LMI toolbox or the open resource software program programs YALMIP and CVX. LMIs at the present time has been a true process. With the aid of the LMI options on top of things platforms research and layout, a growing number of theoretical and functional purposes can now be solved, a lot of which would now not be another way solved by way of conventional equipment. target of the e-book The objective of this publication is to supply a textbook for graduate and senior undergraduate classes within the box of regulate platforms research and layout, which includes the fundamental yet systematic wisdom approximately LMIs and LMI-based keep watch over platforms research and layout. Boyd et al. (1994), that's the 1st booklet on LMIs, definitely has played a pioneering functionality within the box, yet constrained through time it fails to meet up with the ever quickly rising new theories and strategies in LMIs. Yu (2002) is a e-book on LMI method of powerful keep watch over, that is appropriate for use as a textbook, however the chinese limits its utilization around the globe"
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Additional info for LMIs in control systems : analysis, design and applications
Sample text
1981) and Boyd and Barratt (1991). Furthermore, a detailed history of the development of ellipsoid algorithm, including English and Russian references, can be found in Chapter 3 of Akgül (1984). Interior-Point algorithms: General interior-point methods were really proposed in the 1960s (Lieu and Huard 1966, Dikin 1967, Huard 1967, Fiacco and McCormick 1968). While for interiorpoint algorithms, solving various LMI problems have been developed in the 1990s by several researchers. The first were Nesterov and Nemirovsky (1988, 1990a,b, 1991, 1993, 1994); others include Alizadeh (1991, 1992a,b), Jarre (1993), Vandenberghe and Boyd (1995), Rendl et al.
4 Advantages Having reviewed the development process of LMIs, we can now give a brief summarization of the advantages of LMI approaches for control systems analysis and design. 3, and will learn from the next chapter, that LMIs form convex constraints, and therefore, many optimization problems involving LMIs 1. are convex, and hence have solvable global optimal solutions 2. can be solved numerically efficiently and reliably 3. are always solvable even when their sizes are very large. So, for an LMI problem, a solution can always be obtained with acceptable precision due to existence of efficient algorithms as long as the problem has a solution.
3 gives our suggestions. Certain sections in Appendix A may be lectured according to the preference of the lecturer. At the end of each chapter, we have given certain exercise problems. We have also worked out all the solutions to these problems. cn, or by contacting the publisher. 1 Let A ∈ Sm . Show that for arbitrary M ∈ Rm×n , A ≤ 0 implies M T AM ≤ 0. 2 (Duan and Patton 1998, Zhang and Yang 2003, p. 175) Let A ∈ Cn×n . Show that A is Hurwitz stable if A + AH < 0. 3 (Duan and Patton 1998) Let A ∈ Rn×n .