正不変集合を特徴づける密度関数を用いた状態空間の所定領域における非線形システムの解析 [in Japanese] Analysis of Nonlinear Systems in Specified Regions of the State Space by Using Density Functions Characterizing Positively Invariant Sets [in Japanese]
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This paper is concerned with analysis of positive invariance and regional almost convergence of nonlinear systems by using density functions. It is shown that if there exists a density function that is positive inside a set and zero on its boundary then the set is positively invariant and almost all of the trajectories starting from the set are convergent. This result is applicable to controller synthesis for nonlinear systems by using convex optimization with satisfying state and input constraints. Furthermore, converse theorems are provided to ensure the existence of such density functions under mild assumptions.
- Transactions of the Institute of Systems, Control and Information Engineers
Transactions of the Institute of Systems, Control and Information Engineers 19(12), 453-461, 2006-12-15
THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)