A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing in a statisti...

In this paper we study the computation of symmetric systems of bilinear forms over finite fields via symmetric bilinear algorithms. We show that, in general, the symmetric complexity of a system is upper bounded by a constant multiple of the bilinear complexity; we characterize symmetric algorithms in terms of the cosets of a specific cyclic code, and we show that the problem of finding an opti...

In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i....

Bilinear systems can be viewed as a bridge between linear and nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems. This paper provides a formal justification for the extension of interaction matrices to bilinear systems and uses them to express the bilinear state as a linear function of input-output data. Multiple representations of ...

Citation: Kojima K and Takewaki I (2017) Critical Steady-State Response of Single-Degree-of-Freedom Bilinear Hysteretic System under Multi Impulse as Substitute of Long-Duration Ground Motion. Front. Built Environ. 3:41. doi: 10.3389/fbuil.2017.00041 Critical Steady-State Response of Single-Degree-of-Freedom Bilinear Hysteretic System under Multi Impulse as Substitute of Long-Duration Ground Mo...

This paper presents an overview of several gradienttype recursive algorithms for adaptive nonlinear filters equipped with bilinear system models. Bilinear models are attractive because they can approximate a large class of nonlinear systems with great parsimony in the use of coefficients. Two algorithms of complexity O(N3) (N is the memory span of the bilinear system model used in the adaptive ...

A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the differenc...

Hirota’s bilinear technique is applied to some integrable lattice systems related to the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic LotkaVolterra lattice systems, which include the modified Lotka-Volterra lattice system, the modified relativistic Lotka-Volterra lattice system, and the generalized BlaszakMarciniak lattice systems. Determinant solutions are constructe...

This paper presents a comprehensive picture of the mapping of structural properties associated with general linear multivariable systems under bilinear transformation. While the mapping of poles of linear multivariable systems under such a transformation is well known, the question of how the structural invariant properties of a given system are mapped remains unanswered. This paper addresses t...