一类含多面体不确定性多项式系统鲁棒镇定

Robust stabilization for a class of polynomial systems with polytopic uncertainties

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.

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.