Positive Real Analysis Research Articles

Improving transparency of virtual coupling for haptic interaction with human force observer

SUMMARYRelying solely on virtual springs and dampers, the transparency of standard virtual coupling suffers from the device-proxy coordination error when a large interaction force is engaged (e.g., contact tasks) and also from the unmodifiable inertias of the haptic device and the virtual proxy. To overcome these limitations, we propose a novel virtual coupling scheme, which, utilizing passive decomposition and a human force observer, can maintain the device-proxy coordination error even during contact tasks, while also allowing for scaling down (or up) the apparent inertia of the coordinated device-proxy system, thereby, substantially improving transparency of the standard virtual coupling. Experiments are performed to show the performance and passivity of the proposed virtual coupling. Minimum-possible passive inertia scaling is also theoretically established via some positive-real analysis.

Sustainable Youth Let Action Plans for Sri Lankan Youth Unemployment Issues

The researcher vision for the future of Sri Lanka is that it will be a nation where human resource should be utilized at maximum level. For this to be realized, the challenges of youth unemployment must be efficiently addressed. An effective response demands the engagement of all sectors of the nation must contribute to eradicate youth unemployment issues. The researcher proposal for this issue youth-led response with the conviction that, local solutions can positively contribute to surmount the unemployment issues and create youth entrepreneurships. In this research paper, I discuss how youth unemployment affects an individual, local community, town and nation by considering many dimensions. Furthermore, I explain the future efforts must be taken by key stake holders such as government, private and youth entrepreneurs. I have extensively explained youth unemployment problem identification, reasons for unemployment, employment creation, youth entrepreneurship, stake holder’s contribution, suggestions to tackle unemployment problem (Youth let Action Plans). Further, a survey was conducted among the youth in various age categories by focusing many aspects. I hope that, this survey definitely a positive real analysis in the current situation. Further I hope this survey would be a role model to surmount the youth unemployment problem of Sri Lanka and other similar country.

New characterisations of positive realness and static output feedback control of discrete-time systems

This article is concerned with the problems of positive real analysis and control synthesis for discrete-time systems. New linear matrix inequality (LMI) characterisations of positive realness are derived, which enable one to check the positive realness by using parameter-dependent Lyapunov function. The relationship between the proposed characterisations and the existing ones are clarified, which shows that our new results are of less conservatism for characterising the positive realness of discrete-time systems with polytopic uncertainty. In addition, sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities. Numerical examples are included for illustration.

New characterization of positive realness and control of a class of uncertain polytopic discrete-time systems

This paper deals with the problems of positive real analysis and control synthesis for a class of discrete-time polytopic systems with uncertainties. The systems under consideration are modelled in a polytopic form with linear fractional uncertainties in its vertices. A new linear matrix inequality (LMI) characterization of positive realness for this class of systems is given. It enables one to check the positive realness by using parameter-dependent Lyapunov function. This new characterization exhibits a kind of decoupling between the Lyapunov matrix and the system matrices, which is subsequently exploited for control design. Based on the new result, sufficient conditions with reduced conservatism are obtained. A numerical example is also included to demonstrate the applicability of the proposed results.

Positive real analysis and synthesis of uncertain discrete time systems

The positive real analysis and synthesis problems for a class of uncertain discrete-time systems are considered. The uncertainties are expressed in a linear fractional form. The analysis problem is to characterize conditions for a which the uncertain discrete-time system is positive real for all admissible uncertainties. A linear matrix inequality (LMI)-based analysis result is derived. The synthesis problem is to design linear state-feedback and dynamic output-feedback controllers that robustly stabilize the uncertain discrete-time system and achieve the strict positive realness for the closed-loop transfer functions. It has been established that the problems above can be cast into a class of parameterized strict positive real control problems without uncertainties.

Robust stability analysis using the small gain, circle, positivity, and Popov theorems: a comparative study

The stability robustness of a maximum-entropy controller designed for a benchmark problem is examined. Four robustness tests are used, i.e., small gain analysis, circle analysis, positive real analysis, and Popov analysis, each of which is guaranteed to give a less conservative result than the previous test. The analysis is performed graphically. The Popov test is seen, for this example, to yield highly nonconservative robust stability bounds. The results illuminate the conservatism of analysis based on traditional small-gain type tests and reveal the effectiveness of analysis tests based on Popov analysis and related parameter-dependent Lyapunov functions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>