Boundary feedback control design for systems of linear hyperbolic conservation laws in the presence of boundary measurements affected by disturbances is studied. The design of the controller is performed to achieve input-to-state stability (ISS) with respect to measurement disturbances with a minimal gain. The closed-loop system is analyzed as an abstract dynamical system with inputs. Sufficient conditions in the form of dissipation functional inequalities are given to establish an ISS bound for the closed-loop system. The control design problem is turned into an optimization problem over matrix inequality constraints. Semidefinite programming techniques are adopted to devise systematic control design algorithms reducing the effect of measurement disturbances. The effectiveness of the approach is extensively shown in several numerical examples.

研究了线性双曲守恒定律系统在存在受扰动影响的边界测量的情况下的边界反馈控制设计。执行控制器的设计是为了以最小的增益实现​​针对测量干扰的输入状态稳定性（ISS）。闭环系统被分析为具有输入的抽象动力学系统。给出了耗散函数不等式形式的充分条件，以建立闭环系统的ISS界。在矩阵不等式约束条件下，控制设计问题变成了优化问题。采用半定程序设计技术来设计系统控制设计算法，以减少测量干扰的影响。该方法的有效性在几个数值示例中得到了广泛展示。