Modules / Lectures

Sl.No Chapter Name English
1L1-IntroductionDownload
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2L2-First Order systemsDownload
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3L3-Classification of Equilibrium pointsDownload
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4L4-Lipschitz FunctionsDownload
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5L5-Existence/uniqueness theoremsDownload
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6L6-Existence/uniqueness of solutions to differential equationsDownload
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7L7-Lyapunov theorem on stabilityDownload
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8L8-Extension of Lyapunov's Theorem in different contextsDownload
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9L9-LaSalle's Invariance principle, Barbashin and Krasovski theorems, periodic orbitsDownload
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10L10-Bendixson criterion and Poincare-Bendixson criterion. Example: Lotka Volterra predator prey modelDownload
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11L11-Bendixson and Poincare-Bendixson criteria van-der-Pol OscillatorDownload
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12L12-Scilab simulation of Lotka Volterra predator prey model, van-der-Pol Oscillator Review of linearization, operating point/ operating trajectoryDownload
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13L13-Signals, operatorsDownload
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14L14-Norms of signals, systems (operators), Finite gain L2 stableDownload
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15L15-Nyquist plots and Nyquist criterion for stabilityDownload
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16L16-Interconnection between linear system & non-linearity, passive filtersDownload
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17L17-Passive filters, Dissipation equality, positive real lemmaDownload
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18L18-Positive real lemma proofDownload
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19L19- Definition for positive realness and Kalman Yakubovich-Popov TheoremDownload
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20L20-Kalman-Yakubovich-Popov Lemma/theorem and memoryless nonlinearitiesDownload
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21L21-Loop tranformations and circle criterionDownload
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22L22-Nonlinearities based on circle criterionDownload
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23L23-Limit cyclesDownload
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24L24-Popov criterion continuous, frequency-domain theoremDownload
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25L25-Popov criterion continuous, frequency-domain theoremDownload
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26L26-Describing function methodDownload
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27L27-Describing Function :2Download
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28L28-Describing : optimal gainDownload
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29L29-Describing : optimal gainDownload
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30L30-Describing function : Jump HysteresisDownload
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31L31-Describing functions : sufficient conditions for existence of periodic orbits non existence of periodic orbitsDownload
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32L32-Describing functions for nonlinearitiesDownload
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33L33-Ideal relay with Hysteresis and dead zoneDownload
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34L34-Dynamical systems on manifolds-1Download
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35L35-Dynamical systems on manifolds-2Download
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