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<TITLE>Nonlinear MIMO system (State-Space model)</TITLE>
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<I><A HREF="index.html">NelinSys - a program tool for analysis and synthesis of nonlinear control systems</A></I><HR>
<H2>Nonlinear MIMO system (State-Space model)</H2>
<H3>Block description</H3>
<P ALIGN="JUSTIFY">The block implements a nonlinear MIMO (multiple-input multiple-output) system whose behaviour is defined by nonlinear state-space equations of the form</P>
<CENTER><IMG SRC="stavp_siso_vzorec.gif" ALT="Nonlinear state-space description of the system"></CENTER>
<P ALIGN="JUSTIFY">where <I>x = (x1,x2,...,xN)<SUP>T</SUP></I> is the state vector, <I>u = (u1,u2,...,uM)<SUP>T</SUP></I> is the input vector and <I>y = (y1,y2,...,yP)<SUP>T</SUP></I> is the output vector of the system. Nonlinear functions <I>f(x)</I>, <I>g(x)</I>, <I>h(x)</I> can be specified either by symbolic expressions or by identifiers of symbolic variables defined in MATLAB workspace - see detailed description of block parameters below.</P>
<H3>Block parameters</H3>
<CENTER><IMG SRC="stavp_mimo_dialog.jpg" ALT="Dialog box for block parameters setup"></CENTER>
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<DT><I>System order (number of states, N)</I></DT><DD><P ALIGN="JUSTIFY">Positive integer specifying the number of state variables of the system i.e. the dimension of the system state vector <I>x</I>.</P></DD>
<DT><I>f(x), g(x), h(x) - symbolic expression</I></DT><DD><P ALIGN="JUSTIFY">Symbolic expressions defining the nonlinear functions <I>f(x)</I>, <I>g(x)</I>, <I>h(x)</I> used in the state-space equations. The convention how to write these equations and mathematical operations
within them is the same as the one used by Symbolic Math Toolbox. State variables <U>have to be denoted</U> by the <I>x1</I>, <I>x2</I>, ..., <I>xN</I> symbols. If any of the <I>f(x)</I>, <I>g(x)</I>, <I>h(x)</I> functions is not specified by a symbolic expression but by an identifier of a variable (see below), it is necessary to leave corresponding field blank.</P></DD>
<DT><I>f(x), g(x), h(x) - variable identifier</I></DT><DD><P ALIGN="JUSTIFY">Identifiers of symbolic variables (<I>class sym</I> objects) containing the <I>f(x)</I>, <I>g(x)</I>, <I>h(x)</I> functions used in the state-space description of the system. If any of the <I>f(x)</I>, <I>g(x)</I>, <I>h(x)</I> functions is not specified by an identifier of a variable but by a symbolic expression (see previous parameters), it is necessary to set corresponding field to 0 (zero).</P></DD>
<DT><I>Initial conditions (initial states)</I></DT><DD><P ALIGN="JUSTIFY">Column vector consisting of the values of the system state variables at the beginning of the simulation.</P></DD>
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<H3>See also</H3>
<UL>
<LI><A HREF="stavp_mimoz.html"><I>Nonlinear MIMO system with disturbance</I></A></LI>
<LI><A HREF="stavp_siso.html"><I>Nonlinear SISO system (State-Space model)</I></A></LI>
<LI><A HREF="stavp_sisoz.html"><I>Nonlinear SISO system with disturbance</I></A></LI>
</UL>
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