一类含多面体不确定性多项式系统鲁棒镇定

针对一类含多面体不确定性的多项式系统，研究其局部稳定鲁棒镇定问题。基于多项式平方和(SOS)技术，将该类非线性控制问题转换为凸的SOS规划问题，并通过引入S-procedure技术，保证了所得结论在局部范围内是有效的。同时，结合参数依赖Lyapunov函数方法，给出了该类系统鲁棒性分析与鲁棒镇定控制问题的充分条件，并将其描述为可由SOS规划技术直接求解的状态依赖线性矩阵不等式约束集。最后，通过数值仿真验证了该方法的有效性。

Robust stabilization for a class of polynomial systems with polytopic uncertainties

The sum of squares(SOS) and the S-procedure techniques are used to analyze the local robust stabilization
problems for a class of polynomial systems with polytopic uncertainties. By using the SOS technique, the nonlinear control
problems are converted into convex SOS programming ones. And the S-procedure technique guarantees that the result holds
in a restricted region. Moreover, sufficient conditions are given for the robust stability analysis and robust stabilization control
of the systems based on the parameter dependent Lyapunov function. All these solvability conditions are formulated as a
constraint set of state dependent linear matrix inequalities, which can be solved by semidefinite programming relaxations
based on SOS programming. Finally, a numerical example verifies the effectiveness of the proposed method.