Chapter 1 a number of version illustration (pages 1–40): Mohammed Chadli, Pierre Borne and Bernard Dubuisson
Chapter 2 balance of constant a number of versions (pages 41–64): Mohammed Chadli, Pierre Borne and Bernard Dubuisson
Chapter three a number of version nation Estimation (pages 65–98): Mohammed Chadli, Pierre Borne and Bernard Dubuisson
Chapter four Stabilization of a number of types (pages 99–126): Mohammed Chadli, Pierre Borne and Bernard Dubuisson
Chapter five powerful Stabilization of a number of versions (pages 127–156): Mohammed Chadli, Pierre Borne and Bernard Dubuisson
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Additional info for Multiple Models Approach in Automation
1. Classification using the Kohonen rule This is similar to the previous rule by simply making (t ) 0. From the class centers previously obtained, the classification is brought about by applying the following algorithm for each instance of vector x(t): g arg min wk (t ) x(t ) k wg (t 1) wg (t ) (t )( x(t ) wg (t )) wk (t 1) wk (t ) k g This operation is repeated until the weights are stabilized. 2. Classification using the fuzzy K-means algorithm The fuzzy K-means algorithm enables us to group the elements using an approach which is fuzzy with a certain degree of membership, with each element having the ability to be part of multiple classes.
7a]. Finally, as is an M-matrix (see Appendix 2), then a positive vector exists such that vector = is positive. Consequently, V x t 0. The problem with this method is that it is not easy to obtain an M-matrix. 7a], substitute matrix Sii with Sii Sii , where is a real parameter and is the appropriately sized identity matrix. 7d]. The following example illustrates this heuristic [CHA 02b, CHA 08b]. 1 does not lead us to an M-matrix. Consequently, nothing can be concluded as regards the stability of the system.
3. 78] i =1 This is a static control law based on output feedback. 79] i =1 This control law is continuous and verifies N i ) > 0 . i=1i z(t ) i min( iI n Other nonlinear dynamic control laws based on output feedback have also been studied [HA 03]. The resulting stabilization conditions are in BMI form. Some linearization algorithms have been proposed [BOY 94, HAS 99]. 1. Introduction Our objective in this chapter is to study the stability of multiple models. Numerous studies on the subject have initially been inspired from techniques developed in the linear domain.