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M .task/backlog.data M .task/completed.data M .task/pending.data M .task/undo.data M "Zettelkasten/Permanent Notes/20250829114522-hybrid-systems.md" A "Zettelkasten/Permanent Notes/20250911165736-switched-systems.md" A "Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md" M "Zettelkasten/Permanent Notes/Literature Notes/LIT-20250911143337-multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems.md"
36 lines
1012 B
Markdown
36 lines
1012 B
Markdown
---
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id: 20250911165736
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title: Switched Systems
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type: permanent
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created: 2025-09-11T20:57:36Z
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modified: 2025-09-11T21:09:55Z
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tags: []
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---
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# Switched Systems
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Switched systems are those that mix continuous and discrete
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dynamics. They are systems that are 'multimodal'. This means
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that they can have different continuous dynamic modes.
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I'm borrowing form
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[[multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems]],
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but here's a short description of how they work.
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A prototypical switched system is as follows:
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$$\dot{x}(t)=f_i ( x(t)), \quad i \in Q \simeq {1,...,N}$$
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with two conditions:
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1. Each $f_i$ is globally [[Lipschitz Continuous]]
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2. The i's are picked in a way that there are finite
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switches in finite time.
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There's also this thing called a *continuous switched
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system*. A continuous switched system is one that does not
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change continuous states when a switch occurs. That is to
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say when switching from $i$ to $i'$:
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$$f_i(x(t_i),t_i) = f_{i'}(x(t_{i'}),t_{i'})$$
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