mpt_getCommonSOSLyapFct

MPT_GETCOMMONSOSLYAPFCT Calculates Common SOS Lyapunov function for system with additive disturbance 

 [solution]=mpt_getCommonSOSLyapFct(ctrlStruct,ndeg,Options)

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 DESCRIPTION
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 This function attempts to compute a higher order Sum of Squares Lyapunov
 function
 V(x) which guarantees exponential stability. The following is satisfied
 alpha * x^2 <= V(x(k))<= beta * x^2  
 V(x(k+1)) - V(x(k))<= - rho * x^2      
 (alpha,beta,rho>=0)

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 INPUT
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 ctrl                  - Explicit controller object
 ndeg                  - Degree of Lyapunov function desired (must be even number >=2)
 Options.sossolver     - SOS solver to be used , 0 : Yalmip (default) or 1: SOSTools
 Options.abs_tol       - Absolute tolerance
 Options.epsilon       - This is a tolerance factor which is introduced to turn
                         LMI inequalities into strict inequalities.
 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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 V          - SOS Lyapunov function: Overall polynomial on partition
                
 feasible   - 1: stable or 0: no statement about stability possible
 rho        - the Lyapunov decay rate over the partition
              (is this is less than zero, stability cannot be guaranteed)
              The Lyapunov value decrease Delta V <= - rho * ||x||^2

 see also MPT_GETPWQLYAPFCT,MPT_GETPWQLYAPFCT, MPT_GETQUADLYAPFCT, MPT_GETPWSOSLYAPFCT,MPT_GETSTABFEEDBACK