A Sufficient and Necessary Condition for Stability of A Class of Nonlinear Switched Systems
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摘要: 研究了一类非线性开关系统的二次稳定性问题.首先将系统的二次稳定性转化为等价 的带约束非线性规划问题,给出了系统二次稳定的充分必要条件;然后利用Fritz John条件,将 该充要条件转化为较易检验的以代数方程和不等式的解表示的代数条件,最后举例说明了该代 数条件的使用.
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关键词:
- 非线性开关系统 /
- 二次稳定性 /
- Fritz John条件
Abstract: In this paper, the stability of a class of nonlinear switched systems is studied. First we transform the quadratic stability of systems into an equivalent nonlinear programming with constrains and then give a sufficient and necessary condition for quadratic stability. With Fritz John condition, we change the condition into an algebraic one in terms of the solutions of equations and inequality, which is easy to verify. Finally, an example is presented to demonstrate how the conditions can be applied.-
Key words:
- Nonlinear switched systems /
- quadratic stability /
- Fritz John condition
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