A geometric approach with stability for two-dimensional systems

Abstract

Abstract-In this paper we consider the problem of internal and external stabilisation of controlled invariant and output nulling subspaces via static feedback, for 2-D FornasiniMarchesini models. A computationally tractable procedure for the stabilisation of these subspaces is developed via linear matrix inequality (LMI) techniques. This is a preliminary step towards the solution of so-called disturbance decoupling problems with stability requirements.

Disturbance Decoupling with Preview for Two-Dimensional Systems

“…Before presenting the solution of Problem 2.1, we need some geometric preliminaries for 2-D systems. These are mainly taken from [15]. We begin by considering the autonomous FM system…”

“…[5]. Let V be a subspace of R n and let V be a basis matrix of V. The following are equivalent [15]:…”

“…In the last two decades, many valuable results have been achieved in the attempt to develop a geometric theory for 2-D systems, [5,9,10,13,14,15]. In particular, a geometric approach for 2-D systems was first introduced in [5] to treat 2-D decoupling problems of nonmeasurable and measurable disturbances, but without a guarantee of stability.…”

“…In particular, a geometric approach for 2-D systems was first introduced in [5] to treat 2-D decoupling problems of nonmeasurable and measurable disturbances, but without a guarantee of stability. In [15], new geometric techniques for internal and external stabilisation of controlled invariant and outputnulling subspaces were developed. This lead to a new solution for the two aforementioned decoupling problems, while achieving asymptotic stability of the closed-loop.…”

Behavior of Limit Cycles in Nonlinear Systems

“…He is also with the Kharazmi University, Tehran, IRAN (e-mail: h4477@ hotmail.com). some systems [5] - [9].…”