Linear System Indicators More Low Cost Under The Restriction Of Output Feedback Control

This paper studies a kind of low-cost output feedback control problems for a class of linear continuous-time systems by methods of bilinear matrix inequality (BMI) and linear matrix inequality (LMI). The design goal is that the controller needs as less as control devices under constraints of regional pole assignment, H infinity index and/or output variance upper-bound. This kind of output feedback control is named as low-cost feedback control. Low-cost control problems with different constraints are analyzed, and some valid algorithms are provided according to different constraints. The main contents of this paper are as follows.1) Low-cost output-feedback control with regional pole assignmentA BMI formulation is first provided the pole constrained output feedback control problem, and a mathematical model of low-cost feedback control is given, which is minimizing the m1-norm in all possible feedback matrices. By adding a relaxed variable and following the existing path-following method, an iterative LMI algorithm is proposed to search serials of desired output-feedback matrices. Furthermore, using path-following method again, an algorithm, beginning with the serials of pole constrained output-feedback matrices, is proposed to find a low-cost output feedback matrix by minimizing the m1-norm of feedback matrix elements.2) Low-cost output-feedback control with constraints on pole and varianceThe design problem is formulated in terms of BMI constrained optimization. By perturbation linearization of BMI, an algorithm is proposed to find low-cost output-feedback matrix with constraints on pole assignment and steady output variance.3) Low-cost output-feedback control with pole assignment H-infinite indexThe method to solve pole-constrained output-feedback above is extended to the low-cost output feedback control problems with regional pole placement and H-infinity bound. An iterative algorithm is proposed to solve the low-cost feedback control with the desired constraints.For the three kinds of low-cost control problems considerded, numerical experiments are provided respectively to demonstrate the effectiveness of the provided algorithms. Key words:Linear system, static output-feedback, low-cost control, pole placement, H∞attenuation level, output variance, bilinear matrix inequality, path-following method...