Browsing by Subject "Lyapunov stability"

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    On the discrete adaptive posicast controller
    (IFAC, 2015) Abidi, K.; Yıldız, Yıldıray
    In this paper, we present the discrete version of the Adaptive Posicast Controller (APC) that deals with parametric uncertainties in systems with input time-delays. The continuous-time APC is based on the Smith Predictor and Finite Spectrum Assignment with time-varying parameters adjusted online. Although the continuous-time APC showed dramatic performance improvements in experimental studies with internal combustion engines, the full benefits could not be realized since the finite integral term in the control law had to be approximated in computer implementation. It is shown in the literature that integral approximation in time-delay compensating controllers degrades the performance if care is not taken. In this work, we present a development of the APC in the discrete-time domain, eliminating the need for approximation. In essence, this paper attempts to present a unified development of the discrete-time APC for systems that are linear with known/unknown input time-delays. Performances of the continuous-time and discrete-time APC, as well as conventional Model Reference Adaptive Controller (MRAC) for linear systems with known time-delay are compared in simulation studies. It is shown that discrete-time APC outperforms its continuoustime counterpart and MRAC. Further simulations studies are also presented to show the performance of the design for systems with uncertain time-delay.
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    Solving a stability problem by Polya's four steps
    (Istanbul Aydin University, Engineering Faculty, 2011) Alacacı, C.; Doğruel, M.
    In this paper, we consider the proof of stability of a nonlinear system. We found it useful to employ Polya’s general four step problem solving process to organize and present the solution and our thinking. Polya's ideas can help us become aware of how we think when we solve problems. Reflecting on how we solve a problem allows us make conceptual connections between a problem at hand and the problems we may need to solve in the future.