The concept of inverse systems for standard and positive linear systems is introduced. Necessary and sufficient conditions for the existence of the positive inverse system for continuous-time and discrete-time linear systems are established. It is shown that: 1) The inverse system of continuous-time linear system is asymptotically stable if and only if the standard system is asymptotically stable. 2) The inverse system of discrete-time linear system is asymptotically stable if and only if the standard system is unstable. 3) The inverse system of continuous-time and discrete-time linear systems are reachable if and only if the standard systems are reachable. The considerations are illustrated by numerical examples.
The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical examples and an example of positive electrical circuit.
The global (absolute) stability of nonlinear systems with negative feedbacks and positive descriptor linear parts is addressed. Transfer matrices of positive descriptor linear systems are analyzed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k₁e ≤ f(e) ≤ k₂e for some positive k₁, k₂. It is shown that the nonlinear feedback systems are globally asymptotically stable if the Nyquist plots of the positive descriptor linear parts are located in the right-hand side of the circles (–¹/k₁, –¹/k₂).
The stability of positive linear continuous-time and discrete-time systems is analyzed by the use of the decomposition of the state matrices into symmetrical and antisymmetrical parts. It is shown that: 1) The state Metzler matrix of positive continuous-time linear system is Hurwitz if and only if its symmetrical part is Hurwitz; 2) The state matrix of positive linear discrete-time system is Schur if and only if its symmetrical part is Hurwitz. These results are extended to inverse matrices of the state matrices of the positive linear systems.
Necessary and sufficient conditions for robust stability of the positive discrete-time interval system with time-delays are established. It is shown that this system is robustly stable if and only if one well de?ned positive discrete-time system with time-delays is asymptotically stable. The considerations are illustrated by numerical example.
A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.
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 tests (criterions) for checking the reachability and the observability of positive linear-discrete-time systems are proposed. The tests do not need checking of rank conditions of the reachability and observability matrices of the systems. Simple sufficient conditions for the unreachability and unobservability of the systems are also established.
A new notion of a realization of transfer matrix of (P;Q; V)-cone-system for discrete-time linear systems is proposed. Necessary and sufficient conditions for the existence of the realizations are established. A procedure is proposed for computation of a realization of a given proper transfer matrix T(z) of (P;Q; V)-cone-system. It is shown that there exists a realization of T(z) of (P;Q; V)-cone-system if and only if there exists a positive realization of T(z) = V T(z)Q!1, where V;Q and P are non-singular matrices generating the cones V;Q and P respectively.
A new class of positive fractional 2D hybrid linear systems is introduced. The solution of the hybrid system is derived. The classical Cayley-Hamilton theorem is extended for fractional 2D hybrid systems. Necessary and sufficient conditions for the positivity are established.
The concept of strong stability is extended for positive and compartmental linear systems. It is shown that: 1) the asymptotically stable positive and compartmental systems are strongly stable if the eigenvalues of the system matrix are distinct, 2) electrical circuits consisting of resistances, capacitances (inductances) and source voltages are strongly stable.
Necessary and sufficient conditions for the reachability and observability of the positive electrical circuits composed of resistors, coils, condensators and voltage sources are established. Definitions of the input-decoupling zeros, output-decoupling zeros and input-output decoupling zeros of the positive electrical circuits are proposed. Some properties of the decoupling zeros of positive electrical circuits are discussed.
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 present study aimed to test how common workaholism is and which groups are most targeted in the workplace among Jordanian employees. Additionally, the roles of positive and negative perfectionism in workaholism were investigated. The sample consisted of 686 employees. All of them completed the study instruments. The results showed that the mean of workaholism was around the mean of the cut -off. Additionally, multivariate tests showed that the results of post hoc differences for positive perfectionism were in favor of males, subordinates, those with a bachelor’s degree, those with less than 5 years of experience, and those aged less than 30 years. Furthermore, the differences for negative perfectionism were in favor of those with a bachelor’s degree and subordinates. For workaholism, the differences were in favor of subordinates, public sector employees, married persons, and those with a diploma degree. Finally, the results of hierarchical regression analysis found that positive and negative perfectionism and some demographic variables predicted 12.9% of the variability in workaholism, and the typical hierarchical regression model included positive and negative perfectionism without other demographic variables.
The term positive psychology has recently entered the field of Second Language Acquisition. The article explains the meaning of the term, presents the definitions of positive psychology, its objectives and history. The key part of the article demonstrates the importance of positive psychology in the second language acquisition presenting many connections between the two fields. The author recommends that positive education is introduced in every school and every foreign language classroom.
The minimum energy control problem for the positive descriptor discrete-time linear systems with bounded inputs by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the positivity and reachability of descriptor discrete-time linear systems are given. Conditions for the existence of solution and procedure for computation of optimal input and the minimal value of the performance index is proposed and illustrated by a numerical example.
Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed conditions are compared with the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.
The aim of this paper is to show that a real order generalization of the dissipative concepts is a useful tool to determine the stability (in the Lyapunov and in the input-output sense) and to design control strategies not only for fractional order non-linear systems, but also for systems composed of integer and fractional order subsystems (mixed-order systems). In particular, the fractional control of integer order system (e.g. PIλ control) can be formalized. The key point is that the gradations of dissipativeness, passivity and positive realness concepts are related among them. Passivating systems is used as a strategy to stabilize them, which is studied in the non-adaptive as well as in the adaptive case.
NHST (null hypothesis significance testing) is the most popular statistical paradigm in psychology. Mistakes in interpretation of its assumptions and their consequences are topic for methodological and statistical discussion for over fifty years. Article presents two problems associated with NHST that are particularly prevalent in psychology: identifying non-significant results with research failure and conducting underpowered research. They can contribute to increase in exploiting questionable research practices in order to obtain desirable, significant outcomes. Three practices: p-hacking, HARKing and selective publishing are described, along with analysis of their impact on replication crisis in psychological science.
The positivity and absolute stability of a class of nonlinear continuous-time and discretetime systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of nonlinear systems are also given.
The article is an attempt to analyze the spatio-pedagogical discourse of the German social pedagogy. It represents only a fragment of reflection on the turns in paradigm of place/ space (spatial turn), as pedagogical terms. & e authors seek to answer the question what is the space and place, and what concepts in the field of reflection on the place/space run in the German social pedagogy. The text introduces, inter alia, the relational concept of space developed by Martina Löw, duality of space and the concept of spacing. Active creation of urban space, the spatial dimension of the relationship and its dynamics are subjected to discussion. The article presents critical approach to the notion of transdisciplinary space, and space-oriented social work. Finally, it provides the incentive for in-depth, international analyzes of spatio-pedagogical theories.