Analysis and Design of Hybrid Systems 2006: A Proceedings by Christos Cassandras, Alessandro Giua, Carla Seatzu, Janan

By Christos Cassandras, Alessandro Giua, Carla Seatzu, Janan Zaytoon

This quantity comprises the complaints of ADHS'06: the 2d IFAC convention on research and layout of Hybrid platforms, equipped in Alghero (Italy) on June 7-9, 2006. ADHS is a sequence of triennial conferences that goals to collect researchers and practitioners with a history up to the mark and laptop technological know-how to supply a survey of the advances within the box of hybrid structures, and in their skill to soak up the problem of study, layout and verification of effective and trustworthy keep watch over structures. ADHS'06 is the second one convention of this sequence after ADHS'03 in Saint Malo.

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M } ) and -k(ec, < c2,j (Vj ~ M). According to the result in C a s e 1 and considering the strictly positiveness of q,j (Vj ~ { 1 , . . , z - 1,z + 1 , . . , m } ) , the existence of 6 and 7 can also be guaranteed. On the other hand, as kz = 0, - k j e c = 0. Consequently, - k z e ~ > -cs,~ is always valid. Therefore, 6 and can always be found such that V~c ~ e(W, p) and Vj C M, -kjooc > -cs,j and - k j e c < c2,j. e ~ W l ~ c , j v j - (e~Wb~,j(-u~,j + kjge~), (31) As -kjge~ _> -cs,j, considering the definitions of CS,j and u~(r), we have - k j e ~ > -u~,j ~ -u~,j + kjec < O.

3 ) re(p) a After r - 1 firings tj(~OAj/a) can still b e fired and it is sufficient to fire tj for a q u a n t i t y less or equal to t h a t to reach m ' in one step. [-1 For According to the previous lemma, regardless of the initial token content in a place p, if an u n t i m e d sequence reduces the marking of p by at most a factor 1/a, t h e n an equivalent finite sequence exists in the d t - n e t system. 2. A marking m is reachable in a dtc o n t P N {H, A, m 0 , @} system (with @ satisfying (10)) iff it is reachable in the underlying u n t i m e d c o n t P N system {A/',mo} with a sequence t h a t never empties an already m a r k e d place.

C r , where C - P o s t - P r e is the token flow m a t r i x and cr is the firing count vector. , 1998), which mainly focus on the high-gain design in the low-and-high gain algorithms aiming to achieve b e t t e r t r a n s i e n t control performance. It should be pointed out t h a t c o m m o n assumptions in all these works are t h a t the lower s a t u r a t i o n b o u n d s are negative constants and the u p p e r satu r a t i o n b o u n d s are positive constants. However, in J F timed c o n t P N systems, the lower s a t u r a t i o n b o u n d is zero and the u p p e r s a t u r a t i o n b o u n d depends on system states.

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