@conference {PB04mi,
	title = {Some relations between ergodicity and minimality properties of invariant sets in quantized control systems},
	booktitle = {Bifurcations in nonsmooth and hybrid dynamical systems: analysis, control and applications},
	series = {S.I.C.C. (Societ\&agrave; Italiana Caos e Complessit\&agrave;)},
	year = {2004},
	note = {<p>poster presentation</p>
},
	month = {21-22 October},
	address = {Milan},
	abstract = {<p>Linear dynamical systems controlled by quantized inputs exhibit phenomena which are typically non-linear, including chaotic behaviours. We consider discrete-time single-input models of the type x(k+1)=Ax(k)+bu(k). The construction of invariant sets for this class of hybrid systems is of utmost importance for the stabilization problem. We first review a technique to construct invariant sets when an arbitrary quantized input set is assigned. We hence study minimality properties for invariant sets when inputs take integer values. There is a relation between a so-called strong minimality property and ergodicity of the closed-loop dynamics, in particular, ergodicity implies strong minimality. A condition ensuring strong minimality is given in terms of the coefficients of the characteristic polynomial of the matrix {\textquoteright}A{\textquoteright}. Two examples are presented: the first one shows that strong minimality does not imply ergodicity. The second one shows that our condition for strong minimality is only sufficient: this is done by exhibition of an ergodic dynamics for which our condition is not satisfied.</p>
},
	keywords = {Embedded Control, Robotics},
	author = {B. Picasso and A. Bicchi}
}
