LAUSR

The stochastic singular system is also called the stochastic differential algebraic system, stochastic descriptor system, generalized stochastic system, and stochastic degenerate system (e.g., [1–4]). This type of system is found in numerous fields of application, which include fluid dynamics, the modeling of multi-body mechanisms, finance, inputoutput economics and the problem of protein folding. The theory of stochastic singular systems, in which a special class of linear stochastic singular systems is considered, has been developed recently [1]. The form of the initial function is given, so the corresponding initial value problem is uniquely solvable by applying the theory of generalized stochastic processes. Using white noise and fractional white noise, two illustrative applications are presented in a previously conducted study [2]. The basic question of solvability has been formulated and considered [5, 6]. Moreover, they propose a normalization procedure, and they completely solve the problem of exact controllability for a class of linear stochastic singular systems. The existence and uniqueness of the impulse solution for a type of stochastic singular systems were discussed by applying Laplace transform [7]. However, theorem 5.2.1 of [8] was incorrectly applied, leading to inappropriate conclusion regarding impulse solution. The solution and exact controllability of the degenerate Sobolev equation have been discussed [4]. The impulse terms may exist in the solution for a stochastic singular system. In addition, the exact null controllability gives some internal properties of the system. Consequently, this study considers the concepts of impulse solution and exact null controllability for a type of stochastic singular systems. In particular, it considers the following Ito singular system: