Twelve model questions for model solutions for students and lecturers in control systems

This paper presents a set of exercises for learners in control theory, dynamical systems, and linear systems analysis, targeting undergraduate or graduate engineering students specializing in control, dynamical systems, or applied mathematics. The exercises are designed to help students achieve the following Intended Learning Outcomes: Analyze equilibria and stability in LTI systems, including open-loop and closed-loop configurations; Assess system properties (diagonalizability, controllability) from trajectories and state-space models without explicit computations; Relate structural properties (e.g., diagonalizability) to stability criteria, including BIBO stability and Nyquist-based predictions; Derive state-space models from ODEs and interpret Nyquist plots for stability analysis. The material is suitable for coursework, self-study, or exam preparation in introductory-to-intermediate control theory.