Download Hybrid dynamical systems: controller and sensor switching by Andrey V. Savkin PDF

By Andrey V. Savkin

The world of hybrid dynamical structures (HDS) represents a tough and interesting problem to regulate engineers and is known as "the keep an eye on idea of the next day to come" as a result of its destiny strength for fixing difficulties. This particularly new self-discipline bridges keep an eye on engineering, arithmetic, and machine technological know-how. there's now an rising literature in this subject describing a couple of mathematical versions, heuristic algorithms, and balance standards. besides the fact that, shortly there isn't any systematic concept of HDS. "Hybrid Dynamical platforms" specializes in a finished improvement of HDS concept and integrates effects proven by means of the authors.

The paintings is a self-contained informative text/reference, protecting numerous theoretically fascinating and virtually major difficulties in regards to the use of switched controllers and reading the sensor scheduling challenge. The emphasis is on periods of doubtful platforms as versions for HDS.

Features and issues:

* makes a speciality of the layout of sturdy HDS in a logical and transparent demeanour

* Applies the hybrid regulate structures framework to 2 classical strong keep an eye on difficulties: layout of an optimum solid controller for a linear method and simultaneous stabilization of a set of crops

* provides an in depth therapy of balance and H-infinity keep an eye on difficulties for a category of HDS

* Covers fresh unique effects with whole mathematically rigorous proofs

Researchers and postgraduate scholars on top of things engineering, utilized arithmetic, and theoretical desktop technological know-how will locate this ebook covers the newest effects in this very important sector of analysis. complicated engineering practitioners and utilized researchers operating in parts of keep an eye on engineering, sign processing, communications, and fault detection will locate this publication an updated source.

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Additional resources for Hybrid dynamical systems: controller and sensor switching problems

Sample text

3) Hence, our control strate gy is a rule for switching from one basic contro ller to anoth er. Such a rule const ructs a sequence of symbols {ij}f~l from the state meas urem ent x (-). The sequence {i j } f::::a 1 is called the switch ing sequence. 3).

1). Introd uce the corres pondi ng defini tion of robus t stabil izabil ity via synchron ous contro ller switching. 1), the following two condi tions hold: {i} Any soluti on of the closed-loop system [x(·), u(·)] is defined on (0, +00) and belongs to L2 [0, +00). 1). 1) has the prope rty that x(t) ---r 0 as t ---r +00. 1. 2). 1 ) with any locally square-integrable input w(·). 1). The functi on YH(') is called a storag e functi on. 4 Robust Stabilizability via Synchronous Switching 43 The following theorem shows a connection between the concepts of robust stabilizability and robust stabilizability with a quadratic storage function in the case of synchronous controller switching.

D. max a(x). x:llxll= 1 Because the functi on a(x) is contin uous and a(x) < 0, the maxim um is achieved and ao < 0. 3) holds with the asynchronously switc hing controller defined in the statem ent of the theor em and € = -a. This comp letes the proof of the theor em. 1 Suffi cient Conditions for Robust Stabilizability via Asyn chro nous Controller Switching In this subse ction, we derive some sufficient condi tions for robus t stabilizabi lity with a quadr atic storag e functi on via async hrono us contro ller switching.

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