Sliding Surface Design and lyapunov function

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Shilp Dixit
Shilp Dixit 2013-1-2
I want to design a sliding surface for the sliding mode control for the following surface.
if true
Ms = 310;
Mu = 45;
ks = 20000;
kt = 210000;
bs = 4000;
q = sin(pi*t); % disturbance function
%
%
fs = G(alpha.x4 + (1-alpha).x2); % control input function
%
%
A = [0 1 0 0; -1*kt/Mu -1*bs/Mu ks/Mu bs/Mu; 0 -1 0 1; 0 bs/Ms -1*ks/Ms -1*bs/Ms];
B = [0; -1/Mu; 0; 1/Ms];
C = [0 bs/Ms -1*ks/Ms -1*bs/Ms; 0 0 1 0; 1 0 0 0];
D = [1/Ms; 0; 0];
%
E = [-1; 0; 0; 0];
F = [0; 0; 0];
end
State Space Equations are as follows
xdot = A.x(t) + B.u(t) + E.q(t) y = C.x(t) + D.u(t) + F.q(t)
How do I design a sliding surface for this system and the control function using the lyapunov function approach.

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