We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced by piecewise affine approximations which allow an analytical resolution. The sequence of affine models then forms a sequence of states of a hybrid automaton....

In this paper, we obtain some new results on the equi-boundedness of solutions and asymptotic stability for a class nonlinear difference systems with variable delay form x(n+1)=ax(n)+B(n)F(x(n−m(n))), n=0,1,2,...x(n+1)=ax(n)+B(n)F(x(n−m(n))),\ \ n=0,1,2,... where FF is real valued vector function, m:Z→Z+,m:Z→Z+, which bounded function maximum value mm kk k×kk×k coefficient matrix. We carry out ...