Lecture 2��Derivatives, Dynamical Systems & Lyapunov Stability
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Instructor: Ercan Atam
Institute for Data Science & Artificial Intelligence
Course: DSAI 586- Data-Driven Model Predictive Control
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List of contents for this lecture
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Gradient of a scalar function
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Gradient of a vector function: Jacobian
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Derivative of linear transformations (1)
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Derivative of linear transformations (2)
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Derivative for bilinear terms (1)
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Derivative for bilinear terms (2)
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Derivative of quadratic forms (1)
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Derivative of quadratic forms (2)
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Second derivative (Hessian)
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Dynamical systems - time-invariance/time-variance
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Linearization of a dynamical system around an operating point (1)
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Linearization of a dynamical system around an operating point (2)
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Linearization of a dynamical system around an operating point (3)
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Discrete-time dynamical systems
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Linear time-invariant (LTI) discrete-time systems (1)
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Linear time-invariant (LTI) discrete-time systems (2)
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ZOH discretization of linear models (1)
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ZOH discretization of linear models (2)
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ZOH discretization result
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Stability of nonlinear discrete-time systems
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Lyapunov stability definition
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Lyapunov stability illustration
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Asymptotic stability
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Asymptotic stability illustration
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Exponential stability
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Lyapunov function
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Example (1)
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Example (2)
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Definiteness of matrices
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Remarks on definite matrices
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Example
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Equilibrium points for discrete-time LTI systems
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Stability of discrete-time LTI systems (1)
Definition (Stability of discrete-time LTI systems)
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Stability of discrete-time LTI systems (2)
Theorem 1
Theorem 2
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Stability of discrete LTI systems (3)
Theorem 3