CAJ | 학술논문

基于齐次多项式Lyapunov函数这一新工具研究了时变不确定系统鲁棒稳定性问题。针对常见的含参数时变且有界连续可微线性系统的最大稳定区域问题，首先构造常用的参数依赖二次Lyapunov函数，进而给出一个时变系统稳定的充分条件。然后，通过构造适合的参数依赖齐次Lyapunov函数，并利用齐次多项式矩阵表示方法，最终以线性不等式的形式给出系统全局渐近稳定的一个充分条件。数值仿真结果表明齐次Lyapunov函数方法得到的结论对于某些系统比之前类似文献具有更小的保守性。
기우제차다항식Lyapunov함수저일신공구연구료시변불학정계통로봉은정성문제。침대상견적함삼수시변차유계련속가미선성계통적최대은정구역문제，수선구조상용적삼수의뢰이차Lyapunov함수，진이급출일개시변계통은정적충분조건。연후，통과구조괄합적삼수의뢰제차Lyapunov함수，병이용제차다항식구진표시방법，최종이선성불등식적형식급출계통전국점근은정적일개충분조건。수치방진결과표명제차Lyapunov함수방법득도적결론대우모사계통비지전유사문헌구유경소적보수성。
This paper considers the stability analysis of linear continuous-time systems and that the dynamic matrices are affected by uncertain time-varying parameters which are assumed to be bounded continuously differentiable with bounded rates of variation. First sufficient conditions of stability for time-varying systems are given by the commonly used parameter-dependent quadratic Lyapunov function. Moreover the use of homogeneous polynomial Lyapunov functions for the stability analysis of the linear system subject to the time-varying parametric uncertainty is introduced. Sufficient conditions to determine the sought after Lyapunov function is derived via a suitable paramenterization of polynomial homogeneous forms. A numerical example is given to illustrate that the stability conditions are less conservative than similar tests in the literature.