Method of Lyapunovs Function

The method of Lyapunov s function consists of constructing a function V(x,y) with the following properties  

For the steady-state solution of a CSTR, the dynamical equations in terms of deviation variables (Denn, 1975), 

y) is negative definite if the terms in the braces are positive definite. Thus F(x,y) is negative definite if and only if 

The first inequality is true for power law kinetics. The second inequality holds only for certain values of v. Let v, be the value of y such that v - vj is the minimum and for which the second inequality is violated. Then, the stability is ensured for all (u,v) such that 

Other types of Lyapunov s functions may also be constructed. 

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