1
Linear systems
▶
1.1
Observability and controllability matrices
▶
1.1.1
Observability matrix
1.1.2
Controllability matrix
1.1.3
Milestone: observability iff trivial kernel of \(\mathcal{O}\)
1.1.4
Rank characterizations
1.1.5
Hautus observability
1.1.6
Hautus controllability
2
Ordinary differential equations
▶
2.1
Dini derivatives
2.2
Gronwall–Bellman inequality
2.3
Continuous dependence on parameters
2.4
Comparison lemma
3
Lyapunov stability
▶
3.1
Trajectories, equilibria, and comparison functions
3.2
Stability predicates
3.3
Sublevel sets and positive invariance
3.4
Lyapunov functions
3.5
Milestone theorems for autonomous systems
3.6
LaSalle’s invariance principle
3.7
Lyapunov class \(\mathcal{K}\) bounds
3.8
Class \(\mathcal{KL}\) functions and the Osgood construction
Dependency graph
LeanForControl
Anand Gokhale Francesco Bullo
University of California, Santa Barbara
1
Linear systems
1.1
Observability and controllability matrices
1.1.1
Observability matrix
1.1.2
Controllability matrix
1.1.3
Milestone: observability iff trivial kernel of \(\mathcal{O}\)
1.1.4
Rank characterizations
1.1.5
Hautus observability
1.1.6
Hautus controllability
2
Ordinary differential equations
2.1
Dini derivatives
2.2
Gronwall–Bellman inequality
2.3
Continuous dependence on parameters
2.4
Comparison lemma
3
Lyapunov stability
3.1
Trajectories, equilibria, and comparison functions
3.2
Stability predicates
3.3
Sublevel sets and positive invariance
3.4
Lyapunov functions
3.5
Milestone theorems for autonomous systems
3.6
LaSalle’s invariance principle
3.7
Lyapunov class \(\mathcal{K}\) bounds
3.8
Class \(\mathcal{KL}\) functions and the Osgood construction