飽和を有する制御系の解析条件の関係性について:マルティプライア/ポリトープ的方法に基づくL<SUB>2</SUB>/指数安定性能解析 On the Relation between Analysis Conditions for Control Systems with Saturation Nonlinearities:L<SUB>2</SUB>/ Exponential Stability Performance Analysis Based on Multiplier/ Polytopic Approaches
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This paper considers linear time-invariant continuous-time systems with saturation and/ or dead-zone nonlinearities, and proposes analysis methods of a regional L<SUB>2</SUB>and/ or exponential stability performance for the system based on a quadratic Lyapunov function via a multiplier (<I>S</I>-procedure) and a polytopic approaches. In particular, a new domain of L<SUB>2</SUB>/ exponential stability performance is defined by a region of initial states of the system with guaranteed the performance. For the analysis, this paper assumes that the initial state vectors belong to a bounded set and disturbance inputs belong to a set of signals having a bounded L<SUB>2t</SUB> norm. Consequently, the analysis problems using the two approaches can be recast as linear matrix inequality optimization problems respectively. Generally, it is proved that the analysis condition based on the multiplier approach is a sufficient one of the corresponding analysis condition based on the polytopic approach. In the special case of single saturation or dead-zone nonlinearity, it is pointed out that the analysis condition using multiplier approach is exactly the same as the analysis condition using the polytopic approach. Therefore, from the existing result of stability analysis for the system with the single nonlinearity, it is clarified that the analysis condition via the multiplier approach becomes a necessary and sufficient condition of the stability analysis based on the domain of attraction using the quadratic Lyapunov function.
- Transactions of the Society of Instrument and Control Engineers
Transactions of the Society of Instrument and Control Engineers 44(5), 425-433, 2008
The Society of Instrument and Control Engineers