Based On The Bmi Method Static Output Feedback Control Design

Based on Lyapunov stability theory and H_∞control theory, with bilinear matrix inequa-lity (BMI), linear matrix inequality (LMI) and matrix analysis as the mathematical tools,this paper studies static output-feedback for linear time-invariant continuous systems anduncertain linear continuous systems with constraints on pole placement, H_∞attenuationlevel and steady output variance. A BMI formulation is first given for static output feed-back control problem, and then an effective algorithm is proposed to solve the desiredoutput feedback gain.Bounded static output-feedback is first studied for linear continuous systems so thatall poles of the closed-loop systems locate in a given sector area. A new BMI formulationis provided for the solvability of the output-feedback control problem. Then following thespirit of the existing path-following method for solving BMI problem, and an iterative LMIalgorithm is proposed to locally search the desired output-feedback gain. When the poleassignment problem is solvable via output-feedback, the proposed algorithm can likelyoffers a satisfactory feedback gain if the algorithm is started with enough many initialfeedback gains uniformly generated within the admitted range. Furthermore, while theproblem of pole placement admits desired output-feedback, an algorithm is proposed tosolve lower cost output feedback gain, which also places all the poles of the closed-loopsystem to the given area, by minimizing the sum of the absolute of the gain matrixelements. The similar study is extended to uncertain system.And then, the above method to solve pole-constrained output-feedback is extendedrespectively to the problems with regional pole placement and H-infinity bound, and probl-ems with regional pole placement and variance upper-bound. LMI iterative algorithms areproposed to solve the associated problems respectively. Moreover, for continuous time-invariant system, a LMI iterative algorithm is also given to solve the H-infinity output-feedback gain under constraints of regional pole assignment.Numerical experiments demonstrate the effectiveness of the provided algorithms foroutput-feedback problems with constraints on regional pole placement, pole and H-infinity,pole and variance upper bound.