| A central issue in control system design has been to deal with uncertainty and nonlinearity in the systems. In this dissertation, an integrated treatment for both uncertainty and nonlinearity is proposed. This dissertation consists of two relatively independent parts. The first part deals with uncertain linear systems, while the second part treats uncertain nonlinear systems.;In the first part, the problem of control synthesis of uncertain linear systems is considered. A linear fractional transformation (LFT) framework is proposed for robust control design of uncertain linear control systems with structured uncertainty. Robustness synthesis problems are characterized in terms of linear matrix inequalities (LMIs) in the LFT framework. A separation principle for the control synthesis of uncertain linear systems is revealed.;In the second part, the problem of control synthesis for nonlinear systems is addressed; stabilization, ${cal L}sp1$-control, ${cal H}sb{infty}$-control, robustness analysis, and robustness synthesis problems for nonlinear systems are examined in detail. In particular, Youla-parameterizations of stabilizing controllers for nonlinear systems are derived. Both nonlinear ${cal L}sp1$-control and nonlinear ${cal H}sb{infty}$-control are also considered for dealing with disturbance attenuation problems for nonlinear systems. The ${cal L}sp1$-performance and ${cal L}sp1$-control of nonlinear systems are characterized in terms of certain invariance sets of the state space. A systematic treatment for ${cal H}sb{infty}$-control synthesis of nonlinear systems is provided; the nonlinear ${cal H}sb{infty}$-control problem is characterized in terms of Hamilton-Jacobi Inequalities (HJIs) and nonlinear matrix inequalities (NLMIs); a class of ${cal H}sb{infty}$-controllers are parameterized. Finally, the problems of stability and performance robustness analysis and synthesis for uncertain nonlinear systems subject to structured perturbations with bounded ${cal L}sb2$-gains are introduced; they are characterized in terms of HJIs and NLMIs as well. Computational issues are also addressed; it is confirmed that the computation needed for robustness analysis and synthesis of nonlinear systems is of equivalent difficulty to that for checking Lyapunov stability. |
