MPT_GETCOMMONLYAPFCT Computes common Lyapunov function for PWA system
[LP,feasible]=mpt_getCommonLyapFct(Fi,Ain,Bin,Options)
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DESCRIPTION
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This function attempts to compute a quadratic Lyapunov function V(x)=x'lPx
which guarantees exponential stability.
PWQ(x) = x'LPx
PWQ(x(k+1)) - PWQ(x(k)) <= rho * x^2
(i.e. rho must be negative to guarantee exponential stability)
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INPUT
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Fi - optimal feedback law given by u=Fi{i}*x
Ain, Bin - system dynamics are given by x(k+1)=Ain{l}x(k)+Bin{l}u(k)
In case of polytopic uncertainty, you may pass a whole cell array
with different dynamics. This function will then attempt to
identify a Lyapunov function with negative decay for all dynamics
in the cell array.
Options.abs_tol - Absolute tolerance
Options.lpsolver - Which LP solver to use (see help mpt_solveLP)
Options.debug_level - If this is set to 1, the solution provided by the LMI
solver will be double-checked manually. We strongly
advise to set this to 1, since we've experienced
numerous numerical issues with certain LMI solvers.
Note: If Options is missing or some of the fields are not defined, the default
values from mptOptions will be used
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OUTPUT
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LP - Quadratic Lyapunov function: Q(x)=x'LP{r}x%
feasible - 1: stable 0: no statement about stability possible
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LITERATURE
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Automatica, Volume 38, issue 12, pp. 2139 - 2146
"Analysis of discrete-time piecewise affine and hybrid systems",
Ferrari-Trecate G., F.A. Cuzzola, D. Mignone and M. Morari,
see also MPT_GETPWQLYAPFCT, MPT_GETSTABFEEDBACK