Bulletin of the Polish Academy of Sciences Technical Sciences

Spectral properties of nonnegative and Metzler matrices are considered. The conditions for existence of Metzler spectrum in dynamical systems have been established. An electric RL and GC ladder-network is presented as an example of dynamical Metzler system. The suitable conditions for parameters of these electrical networks are formulated. Numerical calculations were done in MATLAB.

A new concept (notion) of the practical stability of positive fractional discrete-time linear systems is introduced. Necessary and sufficient conditions for the practical stability of the positive fractional systems are established. It is shown that the positive fractional systems are practically unstable if corresponding standard positive fractional systems are asymptotically unstable.

New frequency domain methods for stability analysis of linear continuous-time fractional order systems with delays of the retarded type are given. The methods are obtained by generalisation to the class of fractional order systems with delays of the Mikhailov stability criterion and the modified Mikhailov stability criterion known from the theory of natural order systems without and with delays. The study is illustrated by numerical examples of time-delay systems of commensurate and non-commensurate fractional orders.

Simple new necessary and sufficient conditions for asymptotic stability of the positive linear discrete-time systems with delays in states are established. It is shown that asymptotic stability of the system is equivalent to asymptotic stability of the corresponding positive discrete-time system without delays of the same size. The considerations are illustrated by numerical examples.

The paper presents the stability problem of control systems composed of a fractional-order PI controller and a inertial plant of a fractional order with time delay. Simple and efficient computational method for determining stability regions in the controller and plant parameters space is given. Knowledge of these regions permits tuning of the fractional-order PI controller. The method proposed is based on the classical D-partition method.

In the present paper finite-dimensional dynamical control systems described by semilinear ordinary differential state equations with multiple point delays in control are considered. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Using so-called generalized open mapping theorem, sufficient conditions for constrained local relative controllability near the origin are formulated and proved. Roughly speaking, it will be proved that under suitable assumptions constrained global relative controllability of a linear associated approximated dynamical system implies constrained local relative controllability near the origin of the original semilinear dynamical system. This is generalization to the constrained controllability case some previous results concerning controllability of linear dynamical systems with multiple point delays in the control and with unconstrained controls. Moreover, necessary and sufficient conditions for constrained global relative controllability of an associated linear dynamical system with multiple point delays in control are discussed. Simple numerical example, which illustrates theoretical considerations is also given. Finally, some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.

In the paper the parallel compensator considered in [1] is applied to control of the plants with delay and compared with Smith predictor. It is noted that Smith predictor removes only the delay, while the parallel compensator also changes the dynamics of the replacement plant; the latter may be in some degree of freedom shaped by the designer. Owing to this the transients of the system with parallel compensator are significantly faster. Accounting implementability, the control saturations are introduced in control algorithms. Additionally it is shown that using parallel compensator we may apply a relay control to the plants with delay and nonminimum phase zeros, which is impossible by using Smith predictor. Several results of simulations are described which confirm these observations.

Together with the dynamic development of modern computer systems, the possibilities of applying refined methods of nonparametric estimation to control engineering tasks have grown just as fast. This broad and complex theme is presented in this paper for the case of estimation of density of a random variable distribution. Nonparametric methods allow here the useful characterization of probability distributions without arbitrary assumptions regarding their membership to a fixed class. Following an illustratory description of the fundamental procedures used to this end, results will be generalized and synthetically presented of research on the application of kernel estimators, dominant here, in problems of Bayes parameter estimation with asymmetrical polynomial loss function, as well as for fault detection in dynamical systems as objects of automatic control, in the scope of detection, diagnosis and prognosis of malfunctions. To this aim the basics of data analysis and exploration tasks - recognition of outliers, clustering and classification - solved using uniform mathematical apparatus based on the kernel estimators methodology were also investigated

The paper considers a digital design of time-invariant systems in the case of step-invariant (ZOH), bilinear (Tustin's) and fractional order hold (FROH) discretization methods. The design problem is formulated as linear matrix inequalities (LMI). A closed-loop stability of the digitally designed control systems is discussed.

This paper presents a brief survey of our research in which we have used control theoretic methods in modelling and control of cancer populations. We focus our attention on two classes of problems: optimization of anticancer chemotherapy taking into account both phase specificity and drug resistance, and modelling, and optimization of antiangiogenic therapy. In the case of chemotherapy the control action is directly aimed against the cancer cells while in the case of antiangiogenic therapy it is directed against normal cells building blood vessels and only indirectly it controls cancer growth. We discuss models (both finite and infinite dimensional) which are used to find conditions for tumour eradication and to optimize chemotherapy protocols treating cell cycle as an object of control. In the case of antiangiogenic therapy we follow the line of reasoning presented by Hahnfeldt et al. who proposed to use classical models of self-limiting tumour growth with variable carrying capacity defined by the dynamics of the vascular network induced by the tumour in the process of angiogenesis. In this case antiangiogenic protocols are understood as control strategies and their optimization leads to new recommendations for anticancer therapy.

This article describes queueing systems and queueing networks which are successfully used for performance analysis of different systems such as computer, communications, transportation networks and manufacturing. It incorporates classical Markovian systems with exponential service times and a Poisson arrival process, and queueing systems with individual service. Oscillating queueing systems and queueing systems with Cox and Weibull service time distribution as examples of non-Markovian systems are studied. Jackson's, Kelly's and BCMP networks are also briefly characterized. The model of Fork-Join systems applied to parallel processing analysis and the FES approximation making possible of Fork-Join analysis is also presented. Various types of blocking representing the systems with limited resources are briefly described. In addition, examples of queueing theory applications are given. The application of closed BCMP networks in the health care area and performance evaluation of the information system is presented. In recent years the application of queueing systems and queueing networks to modelling of human performance arouses researchers' interest. Hence, in this paper an architecture called the Queueing Network-Model Human Processor is presented.

This paper gives the simple algorithm for calculation of the degree and coefficients of the minimal polynomial for the complex matrix A = [aij]n x n .

Embedded software and dedicated hardware are vital elements of the modern world, from personal electronics to transportation, from communication to aerospace, from military to gaming, from medical systems to banking. Combinations of even minor hardware or software defects in a complex system may lead to violation of safety with or even without evident system failure. a major problem that the computing profession faces is the lack of a universal approach to unite the dissimilar viewpoints presented by computer science, with its discrete and mathematical underpinnings, and by computer engineering, which focuses on building real systems and considering spatial and material constraints of space, energy, and time. Modern embedded systems include both viewpoints: microprocessors running software and programmable electronic hardware created with an extensive use of software. The gap between science and engineering approaches is clearly visible in engineering education. This survey paper focuses on exploring the commonalities between building software and building hardware in an attempt to establish a new framework for rejuvenating computing education, specifically software engineering for dependable systems. We present here a perspective on software/hardware relationship, aviation system certification, role of software engineering education, and future directions in computing.

Information Technologies (IT) are most and most important factor in economical and social development of particular countries and of the whole world, therefore we often think and told about so called Information Society (IS) as a new form of socio-economical organization of the society. Most properties of IT are profitable for the people and most features of IS are positive. Nevertheless we can find also some problems arising because of too fast development of IT and some dangers connected with increasing dependability of present society on IT devices and services. In the paper selected problems connected with distance teaching and distance learning (so called elearning) are pointed out and considered. As a most important problem so called "information smog" is pointed. It is very troublesome at present and may be source of big problem in the future.