Approximation Entree-Sortie D’un Systeme Non Lineaire Continu par un Systeme Discret

Abstract

It is shown that the input-output map associated to the system

EquationSource<m:math display=&#x2019;block&#x2019;> <m:semantics> <m:mtable columnalign=&#x2019;left&#x2019;> <m:mtr> <m:mtd> <m:mover accent=&#x2019;true&#x2019;> <m:mi>x</m:mi> <m:mo>&#x02D9;</m:mo> </m:mover> <m:mo>=</m:mo><m:mi>f</m:mi><m:mo stretchy=&#x2019;false&#x2019;>(</m:mo><m:mi>x</m:mi><m:mo></m:mo><m:mi>u</m:mi><m:mo stretchy=&#x2019;false&#x2019;>)</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mi>y</m:mi><m:mo>=</m:mo><m:mi>h</m:mi><m:mo stretchy=&#x2019;false&#x2019;>(</m:mo><m:mi>x</m:mi><m:mo stretchy=&#x2019;false&#x2019;>)</m:mo> </m:mtd> </m:mtr> </m:mtable> </m:math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\eqalign{ & \dot x = f(x,u) \cr & y = h(x) \cr} $$

(1)

initialized at an equilibrium point can be approximated by a family of discrete-time state-affine systems of state space of finite dimension. To do this, a sampled system which reproduces the state and output evolutions of system (1) for inputs which are constant on time intervals of fixed amplitude is.computed. The corresponding sampled Volterra series can be approximated by a finite number of kernels, each of these being realized, according to a previous result proposed by the authors for discrete-time systems, by a discrete-time state-affine system. Finally, an example is discussed.