This paper studies the readability property of continuous-time bilinear i/o equations in the classical state space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. The paper proves that the 2nd order bilinear i/o differential equation, unlike the discrete-time case, is always realizable in the classical state space form. The complete list of 3rd and 4th order realizable i/o bilinear models is given and two subclasses of realizable i/o bilinear systems are suggested. Our conditions rely basically upon the property that certain combinations of coefficients of the i/o equations are zero or not zero. We provide explicit state equations for all realizable 2nd and 3rd order bilinear i/o equations, and for one realizable subclass of bilinear i/o equations of arbitrary order.
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机译:本文研究了经典状态空间形式的连续时间双线性I / O方程的可读性性能。提出了对Bilinear I / O模型参数的约束,导致可实现的模型。本文证明,与离散时间外壳不同,第二阶Bilinear I / O差分方程始终可在经典状态空间形式中实现。给出了第3和第4阶可实现的I / O Bilinear模型的完整列表,并提出了可实现的I / O双线性系统的两个子类。我们的条件基本上依赖于I / O等式的系数的某些组合为零或不为零。我们为所有可实现的第二和第3级Bilinear I / O方程提供显式状态方程,以及任意顺序的双线性I / O方程的一个可实现的子类。
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