in this paper a new method is introduced and investigated for removing the destabilizing effects of time-delay parameter in control loops. the concept of the method is taken from the knowledge concerning the dynamic behaviour of irrational transfer functions (ir-tf), which is discussed and investigated elswhere in frequency response domain and is explained briefly here. ir-tfs, which are well c...

This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems for a given frequency band by a rational function are presented. The optimal param...

In this paper, an innovative algorithm of identification of control system, described by irrational transfer function with distributed parameter characteristics with irrational components, is proposed. Algorithm is based on real interpolation method (RIM). Parameters of irrational transfer function can be identified by its experimental transient responses. Each of them can be represented by an ...

Abstract. Classes of irrational function classes, denoted by AS, that lie between the extreme cases of the disk algebra A and the Hardy space H∞(D), are considered. The corona theorem holds for AS, and the following properties are shown: AS is an integral domain, but not a Bézout domain, AS is a Hermite ring with stable rank 1, and the Banach algebra AS has topological stable rank 2. Consequenc...

In this paper a new method is introduced and investigated for removing the destabilizing effects of time-delay parameter in control loops. The concept of the method is taken from the knowledge concerning the dynamic behaviour of irrational transfer functions (Ir-TF), which is discussed and investigated elswhere in frequency response domain and is explained briefly here. Ir-TFs, which are we...

This paper considers H∞-control of infinitedimensional systems whose transfer functions are expressible as the cascade connection of a rational transfer matrix and a scalar (possibly irrational) inner function. This class of systems is very suitable for describing many control problems in practice, when weighting functions are rational and plants have at most finitely many unstable modes. We sh...

In this paper we introduce a method that allows one to prove uniform local results for one-dimensional discrete Schrödinger operators with Sturmian potentials. We apply this method to the transfer matrices in order to study the Lyapunov exponent and the growth rate of eigenfunctions. This gives uniform vanishing of the Lyapunov exponent on the spectrum for all irrational rotation numbers. For i...

In this paper, H∞ control for a class of linear time invariant systems with infinitely many unstable poles is considered. An example of such a plant is a high gain system with delayed feedback. We formulate the problem via a generalized plant which consists of a rational transfer matrix and the inverse of a scalar (possibly irrational) inner function. It is shown that the problem can be separat...