Linear Quadratic Optimal Control: Analysis and Solution

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Dynamics on Homogeneous Spaces and Interactions with Number Theory

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Classification of Quadratic Forms

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Nyquist Stability Criteria

Explains Nyquist stability criteria and loop shaping for system performance and robustness.

State-Space Representation: Controllability and Observability

Explores state-space representation, controllability, observability, and regulator calculation using the Ackermann method.

Stability of ODE

Explores the stability of Ordinary Differential Equations, focusing on solution dependence, critical data, linearization, and control of nonlinear systems.

Dynamic Programming: Optimal Control

Explores Dynamic Programming for optimal control, focusing on stability, stationary policy, and recursive solutions.

State Observers and Output-Feedback Controllers

Covers the design and implementation of state observers and output-feedback controllers in multivariable control systems.

Hermitian Spaces: Theory and Applications

Explores the theory of Hermitian spaces and their applications in quadratic forms and codimension 1 spaces.