Abstract of Thesis presented at COPPE/UFRJ as a partial fulfillment of the requirements for the degree of Doctor of Science (D.Sc.)

Optimization of Robust Controllers Using Piecewise Quadratic Lyapunov Functions

Heraldo Luís Silveira de Almeida

February/2003

Advisors:

Eugenius Kaszkurewicz Djalma Mosqueira Falcão

Department:

Eletrical Engineering

      This work proposes the use of a team algorithm for robust stability analysis and control design of uncertain time-varying linear systems, based on piecewise quadratic simultaneous Lyapunov functions. The objective is to use robust stability criteria that are less conservative than the usual quadratic stability criterion. The use of piecewise quadratic Lyapunov functions leads to a nonconvex optimization problem, which is decomposed into a convex subproblem in a selected subset of decision variables, and a lower dimensional nonconvex subproblem in the remaining decision variables. A team algorithm that combines genetic algorithms and interior-point methods for linear matrix inequalities is proposed as a solution method. The proposed techniques are applied to the design of power system damping controllers. Computational results that are less conservative than those obtained by the quadratic stability criterion are presented for three examples of dynamical systems extracted from the literature. The application of the proposed techniques to the design of power system stabilizers is described, and computational results obtained for two examples of electric power networks are presented.