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Lecture
1st Harmonic: Stability and Adaptation
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Stability of ODE
Explores the stability of Ordinary Differential Equations, focusing on solution dependence, critical data, linearization, and control of nonlinear systems.
Lyapunov Stability Theory: Energy Functions and Stability Analysis
Covers Lyapunov stability theory, energy functions, positive-definite matrices, and system stability analysis through examples and theorems.
Signal and System Analysis: Impulse Response and Convolution
Covers the analysis of LTI systems using impulse response and convolution.
Linear Systems: Direct Methods
Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.
Stability and Reachability in Multivariable Control
Explores stability, reachability, and controllability in linear systems, emphasizing their significance in system analysis.
Nonlinearity: Methods and Examples
Explores nonlinearity in numerical flow simulation, covering linearization methods and practical examples.
Passivity in Linear Systems
Explores passivity in linear systems, discussing conditions for stability and system behavior.
SISO Polynomial Controllers: Sylvester Matrix, Internal Model Principle
Covers the design of SISO polynomial controllers using concepts such as the Sylvester matrix and model matching.
BIBO Stability: Criteria and Analysis
Covers BIBO stability criteria, feedback impact, and system analysis.
Linear Systems: Continuous Time
Covers linear systems in continuous time, stability analysis, and mass-spring system examples.