By Laurent El Ghaoui, Silviu-Iulian Niculescu
Linear matrix inequalities (LMIs) have lately emerged as beneficial instruments for fixing a couple of keep an eye on difficulties. This ebook presents an updated account of the LMI technique and covers issues equivalent to fresh LMI algorithms, research and synthesis matters, nonconvex difficulties, and purposes. It additionally emphasizes functions of the strategy to parts except keep an eye on. the elemental notion of the LMI process up to the mark is to approximate a given keep an eye on challenge through an optimization challenge with linear aim and so-called LMI constraints. The LMI process ends up in a good numerical answer and is especially fitted to issues of doubtful facts and a number of (possibly conflicting) standards.
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Extra resources for Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control)
Is a strictly increasing infinite sequence of time instants, which determine when the (otherwise smooth) trajectory suddenly jumps from x(r~) to X(T*). By proper choice of the impulse matrix M, one seeks to guarantee stability, using small impulses at properly chosen time instants. 6. Illustrations in control 27 The stability analysis of impulse systems is nontrivial in general. In , Yang and Chua have devised (based on an earlier result by ) a stability criterion, using quadratic Lyapunov functions.
With the matrices Ai of the polytopic model, we associate a "transition probability matrix" that describes the probability of change from one mode to the other. Similarly, it is possible to consider a linear-fractional model, where the uncertain matrix A obeys a known white-noise-type distribution; see  for an example. The reader should not make a conflict out of the distinction deterministic/stochastic: it is possible to consider stochastic models with deterministic uncertainty. For example, we may consider a linear system with Markovian jumps, where the transition probability matrix is unknown-but-bounded (see ).
In classical control, hybrid systems are very common: they arise when one controls a (continuous-time) system with a discrete-time controller. A typical impulse linear differential system is of the form where A, M are given square n x n matrices, and r», i = 0, 1, . . , is a strictly increasing infinite sequence of time instants, which determine when the (otherwise smooth) trajectory suddenly jumps from x(r~) to X(T*). By proper choice of the impulse matrix M, one seeks to guarantee stability, using small impulses at properly chosen time instants.
Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control) by Laurent El Ghaoui, Silviu-Iulian Niculescu