| The design of low-order stabilizing controllers for Linear Time-Invariant (LTI) or Linear Parameter-Varying (LPV) systems which optimize certain closed-loop system performance indices such as pole-placement and H infinity/H2 norms is an NP-hard nonconvex problem in control theory. It requires solving either nonlinear coupled matrix equations, or Bilinear Matrix Inequalities (BMI), or Linear Matrix Inequalities (LMI) with a non-convex rank condition. As a result, the computational complexity of the design is generally very high.; The thesis addresses the problems of designing practical low-order stabilizing controllers with various stability and structural constraints, including static output feedback, LTI Single-input Single-output (SISO), LTI Multi-input Multi-output (MIMO), and LPV controllers. A systematic approach to solve for a subset of these design problems is proposed in the thesis. An important step of the approach is to make use of coprime factors so that the design of low-order controllers with various structures can be formulated as LMI feasibility or optimization problems. Furthermore, these LMIs are also sufficient for the existence of Lyapunov functions, which can be either fixed or parameter dependent, to establish the closed-loop system stability.; This new approach only requires the solution to LMIs to obtain low-order stabilizing controllers, which can be solved with efficient semi-definite programming algorithms with the complexity no worse than polynomial time. Using the results on low-order stabilizing controller designs as building blocks, algorithms are proposed for designing low-order controllers for several important problems including simultaneous stabilization, regional pole-placement, and Hinfinity/H2 sub-optimal control.; One of the advantages of the approach is that its computational cost is much lower than the existing approaches based on iterative solutions of BMI or LMI with a non-convex rank condition. Another advantage is that many important constraints on controller structures, such as decentralization, integral action, differential action, strong stabilization, and minimal phase, can be directly accommodated in the proposed algorithms.; The proposed algorithms have been successfully applied to the design of low-order controllers for several well-known problems. Simulation results illustrate the merits of the new approach. |
