SOS_1.rar_MATLAB sostools_SOS_SOSTOOLS_SOSTOOLS工具箱_系统稳定性

% SOSDEMO2 --- Lyapunov Function Search % Section 3.2 of SOSTOOLS User's Manual % clear; echo on; pvar x1 x2 x3; vars = [x1; x2; x3]; % Constructing the vector field dx/dt = f f = [(-x1^3-x1*x3^2)*(x3^2+1); (-x2-x1^2*x2)*(x3^2+1); (-x3+3*x1^2*x3)*(x3^2+1)-3*x3]; % ============================================= % First, initialize the sum of squares program %the following was used to test the sosprogram function by passing the decision variables as an argument GV %syms dec1 dec2; %decvartable = [dec1; dec2]; %prog = sosprogram(vars,decvartable); %which is replacing the previous command prog = sosprogram(vars); % ============================================= % The Lyapunov function V(x): [prog,V] = sospolyvar(prog,[x1^2; x2^2; x3^2],'wscoeff'); % ============================================= % Next, define SOSP constraints % Constraint 1 : V(x) - (x1^2 + x2^2 + x3^2) >= 0 prog = sosineq(prog,V-(x1^2+x2^2+x3^2)); % Constraint 2: -dV/dx*(x3^2+1)*f >= 0 expr = -(diff(V,x1)*f(1)+diff(V,x2)*f(2)+diff(V,x3)*f(3)); prog = sosineq(prog,expr); % ============================================= % And call solver prog = sossolve(prog); % ============================================= % Finally, get solution SOLV = sosgetsol(prog,V) echo off;