Effectiveness and Limitation of Polytopic Approach for Quadratic Performance Analysis/Synthesis with Saturating Control
Tsuyoshi KIYAMA, Mitsuyoshi TAKENAKA
This paper considers a regional quadratic performance analysis and state feedback synthesis method based on a polytopic approach for linear time invariant systems with saturation nonlinearities. In particular, a domain of quadratic performance is defined as a region of initial states in order to satisfy a quadratic performance. In the analysis case, the polytopic approach is theoretically less conservative than both the circle criterion and the existing linear analysis. However, in the synthesis case, the synthesis condition with the polytopic approach is theoretically equivalent to one with the circle criterion or the linear analysis in the meaning of the same achievable domains or quadratic performance levels in spite of obtaining different state feedback controllers respectively. Finally, this paper proposes a synthesis method making use of effectiveness of the polytopic approach.