Engineering perspective of ecological sign stability and its application in control design

In this paper, we provide an engineering perspective of ecological sign stability and its use in control design for engineering systems. In particular, using purely ecological principles, we propose novel, tight bounds on the real and imaginary parts of the eigenvalues of a sign stable matrix in terms of the elements of the matrix. The simplicity of these bounds has interesting implications in computational mathematics. Using the special features of predator-prey interaction in sign stable matrices for eigenvalues and condition number properties, it is established that predator-prey interactions improve robustness properties. Motivated by this, a new control design algorithm is proposed for linear systems. `Sign assignability conditions´ are derived to guarantee the existence of the controller that yields a sign stable closed loop system. This algorithm takes full advantage of the concepts of ecological sign stability that results in a highly robust engineering system. The proposed control design method is then illustrated with examples in satellite attitude control and aircraft light control.