In this paper, we present a study on mean square approximate controllability and finite-dimensional exact for the system governed by linear/semilinear infinite-dimensional stochastic evolution equations. We introduce resolvent-like operator and, using operator, formulate criterion finite-approximate of linear systems. A control is also found that provides in addition to requirement controllabil...

The Ablowitz-Ladik hierarchy (ALH) is considered in the framework of the inverse scattering approach. After establishing the structure of solutions of the auxiliary linear problems , the ALH, which has been originally introduced as an infinite system of difference-differential equations is presented as a finite system of difference-functional equations. The representation obtained, when rewritt...

In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...

In this paper, the input-output behavior of a linear stable system is studied in some detail. Some results are presented to make more precise the folklore statement that outputs follow inputs for stable linear systems. Based on these results, it is also discussed how to choose an output and how to fuse a number of sensor outputs, to best trac k the input in stationarit y.

The trajectory tracking problem for multivariable linear systems is considered. Two different techniques are examined: the output regulation theory (ORT) and the flatness based tracking (FBT). ORT and FBT are two different approaches to solve the tracking problem, and both methods have different restrictions. The tracking controller of the ORT furthermore depends on the solution of the so-calle...

this paper presents an operational formulation of the tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(fdes). the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations....

This paper considers the problem of determining whether the observability (or controllability) matrix of a given discrete-time switched linear system reaches full rank for any mode sequence. We show that this problem is in fact decidable, and we provide finite upper bounds on the maximum sequence length at which this property may be satisfied.