A Systematic Method for Backstepping via Linear Matrix Inequalities

In this paper, a systematic method for implementing backstepping via linear matrix inequalities is developed. It is based on using the direct Lyapunov method at each step of the backstepping procedure in order to find a control law as a nonlinear convex sum of gains. These gains are obtained via commercially available software for solving linear matrix inequalities, which guarantees numerical readiness of the proposal. Moreover, dealing with MIMO subsystems at each step can be done without further adjustments. Examples of academic and practical interest illustrate the advantages of the novel methodology over former approaches.