Enlarging Nonlinear Discrete System’s Domain of Attraction Via Linear Control Law

This paper investigates the problem of designing controllers to enlarge the stability domain of polynomial discrete systems. In order to deal with this problem, we propose a method for computing a linear feedback control law, which extends the largest estimate of the stability domain. The designing of the control law is established in the form of an optimization problem that focuses on expanding the stability domain. An application example is presented to illustrate the efficiency of the proposed controller law for maximizing stability domain. The simulation results prove clearly the capability of our linear controller approach to increase the radium of the stability domain for the studied nonlinear system.