Worst-case performance analysis and controller synthesis for lur’e systems with time delays and parametric uncertainties

Abstract

It is well known that the stability is the most fundamental problem in analysis and design of control systems. Once the concept of the nonlinear isolation method is introduced in terms of Lur’e problem, the absolute stability which is the global asymptotically stability of Lur’e systems have been extensively studied and utilized in a number of different contexts. This dissertation presents the analysis and synthesis of Lur’e systems with uncertain time-invariant delays and norm-bounded uncertainties, using linear matrix inequalities (LMIs). The analysis part is devoted to the absolute stability and the worst-case H∞ performance analysis problems. The direct Lyapunov method with a delay-partitioning Lyapunov-Krasovskii functional containing the integral of nonlinearities is applied for determining stability, and calculating an upper bound of the worst-case H∞ performance. Both analyses are formulated as optimization problems involving LMIs which can be efficiently solved. A bisection method associated with LMI optimization is introduced to determine the maximum allowable time delay. The synthesis part involves the state-feedback stabilization and H∞ control problems. Extending the proposed analyses, the controller design problems are first formulated as non-convex optimization problem involving bilinear matrix inequalities (BMIs). We develop algorithms based on coordinate optimization, which alternate between two LMI optimizations, to solve for the robust control problems. Numerical results from benchmark problems including the continuous stirred tank reactor (CSTR) with recycle stream show that the proposed analysis and synthesis give significant improvement on the results comparing to the open-loop response.