Stabilization of Constrained Nonlinear Triangular Delay Systems Using Convex Optimization

Abstract

The possibility is studied of reducing the stabilization problem for delay differential nonlinear system to optimization problems with known numerical procedures for solving. Assuming a triangular structure of the system, algorithms are proposed for constructing a stabilizing control. The description of the subsystems in the form of Takagi–Sugeno models is used. Given the state and control constraints, as well as the properties of weight functions, the stabilization problem is reduced to some optimization problems, including LMIs. The obtained controls retain stabilizing properties for non-stationary weight functions, as well as for perturbed systems. Chances of numerical implementation of algorithms based on standard procedures of computational software are considered.