This paper proposes a polynomially sampled parameter dependent controller design for sampled-data linear parameter varying (LPV) systems. The goal of this study is to design a controller which exponentially stabilizes the system with a larger maximum sampling interval. To achieve this, we utilize the information of the parameters in the controller part. The proposed controller is dependent on the polynomials with respect to the sampled parameters, which is more effective to stabilize the system with a larger maximum sampling interval. To design the controller, an exponential stabilization condition is derived from a new Polynomially Parameter Dependent Quadratic Lyapunov Function with Looped-Functionals (PPDQLLF) which is dependent on the parameters of a plant. The derived condition is represented in terms of the linear matrix inequality (LMI) and it is formulated as sum of squares (SOS) conditions to obtain feasible solutions. The effectiveness of the proposed method is shown by the simulation results of numerical examples.

本文提出了一种用于采样数据线性参数变化 (LPV) 系统的多项式采样参数相关控制器设计。本研究的目标是设计一个控制器，该控制器以更大的最大采样间隔指数稳定系统。为了实现这一点，我们利用了控制器部分的参数信息。所提出的控制器依赖于关于采样参数的多项式，这对于以更大的最大采样间隔稳定系统更有效。为了设计控制器，指数稳定条件是从新的多项式参数相关二次李雅普诺夫函数与循环函数 (PPDQLLF) 中导出的，该函数依赖于设备的参数。导出的条件用线性矩阵不等式 (LMI) 表示，并将其公式化为平方和 (SOS) 条件以获得可行解。数值算例的仿真结果表明了该方法的有效性。