Spring semester 2006 ESE 601: Hybrid Systems Review material on continuous systems I.
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Transcript of Spring semester 2006 ESE 601: Hybrid Systems Review material on continuous systems I.
References
• Kwakernaak, H. and Sivan, R. “Modern signal and systems”, Prentice Hall, 1991.
• Brogan, W., “Modern control theory”, Prentice Hall Int’l, 1991.
• Textbooks or lecture notes on linear systems or systems theory.
Contents
• Modeling with differential equations• Taxonomy of systems• Solution to linear ODEs• General solution concept• Simulation and numerical methods• State space representation• Stability• Reachability
Contents
• Modeling with differential equations• Taxonomy of systems• Solution to linear ODEs• General solution concept• Simulation and numerical methods• State space representation• Stability• Reachability
Linear vs nonlinear
• Linear systems: if the set of solutions is closed under linear operation, i.e. scaling and addition.
• All the examples are linear systems, except for the pendulum.
Time invariant vs time varying
• Time invariant: the set of solutions is closed under time shifting.
• Time varying: the set of solutions is not closed under time shifting.
Autonomous vs non-autonomous
• Autonomous systems: given the past of the signals, the future is already fixed.
• Non-autonomous systems: there is possibility for input, non-determinism.
Contents
• Modeling with differential equations• Taxonomy of systems• Solution to linear ODEs• General solution concept• Simulation and numerical methods• State space representation• Stability• Reachability
Contents
• Modeling with differential equations• Taxonomy of systems• Solution to linear ODEs• General solution concepts• Simulation and numerical methods• State space representation• Stability• Reachability
Contents
• Modeling with differential equations• Taxonomy of systems• Solution to linear ODEs• General solution concepts• Simulation and numerical methods• State space representation• Stability• Reachability
Contents
• Modeling with differential equations• Taxonomy of systems• Solution to linear ODEs• General solution concepts• Simulation and numerical methods• State space representation• Stability• Reachability
State space representation• One of the most important representations of
linear time invariant systems.
Contents
• Modeling with differential equations• Taxonomy of systems• Solution to linear ODEs• Simulation and numerical methods• State space representation• Stability• Reachability• Discrete time systems
Contents
• Modeling with differential equations• Taxonomy of systems• Solution to linear ODEs• General solution concept• Simulation and numerical methods• State space representation• Stability• Reachability