A new form of a &amp;#x03C3;-inverse for nonsquare polynomial matrices

Majewski

2018

J Wireless Com Network

The paper outlines a new approach to the signal reconstruction process in multivariable wireless communications tasks. A new solution is proposed using the so-called Smith factorization, which is efficiently used in the synthesis of control systems described by polynomial matrix notation. In particular, the so-called polynomial S-inverse is used, which, together with the applied degrees of freedom, creates a potential for the improvement of the operation of wireless data communications systems comprising different numbers of inputs/antennas and outputs/antennas. Simulations performed in the Matlab environment indicate the practical applicability of the proposed solution.

Section: Resultsmentioning

confidence: 99%

“…It should be emphasized that the new forms of polynomial right and left σ -inverses (including also the parameter cases) are given in References [24,26] as follows:…”

Section: σ -Inversesmentioning

confidence: 99%

Perfect reconstruction of signal—a new polynomial matrix inverse approach

Majewski

2018

J Wireless Com Network

“…The newest definition of σ-inverse can be found in Ref. [32] in the form of the following corollary Corollary 1. Let the polynomial matrix W(q −1 ) = w 0 + w 1 q −1 + .…”

Section: Inverses Of Nonsquare (Parameter) Matricesmentioning

confidence: 99%

A New Stability Theory for Grünwald–Letnikov Inverse Model Control in the Multivariable LTI Fractional-Order Framework

Wach

2019

Symmetry

The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due to an infinite number of solutions to the underlying inverse problem for nonsquare matrices. Therefore, the paper presents a new algorithm for fractional-order perfect control with corresponding stability formula involving recently given H- and σ -inverse of nonsquare matrices, up to now applied solely to the integer-order plants. On such foundation a new set of stability-related tools is introduced, among them the key role played by so-called control zeros. Control zeros constitute an extension of transmission zeros for nonsquare fractional-order LTI MIMO systems under inverse model control. Based on the sets of stable control zeros a minimum-phase behavior is specified because of the stability of newly defined perfect control law described in the non-integer-order framework. The whole theory is complemented by pole-free fractional-order perfect control paradigm, a special case of fractional-order perfect control strategy. A significant number of simulation examples confirm the correctness and research potential proposed in the paper methodology.

“…For right-invertible systems, the symbol R ( −1 ) denotes, in general, an infinite number of right inverses of the numerator polynomial matrix ( −1 ) (see e.g. [26][27][28][29]). Now, for our queueing model we have…”

Section: Minimum Variance Control Algorithms 41 Closed-loop Discretmentioning

confidence: 99%

New Results in Generalized Minimum Variance Control of Computer Networks

Dzierwa

2014

ITC

In this paper new results in adaptive (generalized) minimum variance control of packet switching computer networks are presented. New solutions, corresponding to the new inverses of the nonsquare polynomial matrices, can be used for design of robust control of multivariable systems with different number of inputs and outputs. Application of polynomial matrix inverses with arbitrary degrees of freedom creates the possibilities to optimal control of computer networks in terms of usage their maximal bandwidth. Simulation examples made in Matlab environment show big potential of presented approach.