A dual to Lyapunov's stability theorem

By Anders Rantzer. 2001

377 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0dbcfff93d9bf6116eb1cf2b1d92411fba79104a

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In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Stability in the almost everywhere sense: A linear transfer operator approach (2010, methodology): “If we choose X = [0,2], Λ = {0}, Bδ = (0,1), ρ0(x) = χ[1,2](x), then φt(x) = xe−t , P1 t ρ(x) = et , t ∈ [0, ln( (2)x )] and the Lyapunov density is the solution of the following d dx ( xρ(x) ) = −1, ρ(2) = 0, x ∈ [1,2].”
Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization (2003, methodology): “Additionally a convex optimization approach using the concept of a dual to the Lyapunov function is provided in [27].”
LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification (2010, background): “This has proven to be a difficult problem because the set of V x and x satisfying these conditions may not be convex or even connected (Rantzer 2001).”
Convex Computation of the Region of Attraction of Polynomial Control Systems (2012, neutral): “, [15], [27], [37], [42] and references therein.”
Nonlinear control synthesis by convex optimization (2004, neutral): “The proof for the other case can be found in [15].”
Nonlinear control synthesis by sum of squares optimization: a Lyapunov-based approach (2004, background): “Because of this, a dual approach to the state feedback synthesis based on density functions [19] has been proposed [18], which has a better convexity property.”
Classical Converse Theorems in Lyapunov's Second Method (2015, methodology): “An approach to almost global asymptotic stability, refered to as a “dual” to Lyapunov’s second method, was presented in [88] with a converse theorem in [89].”
A Differential Lyapunov Framework for Contraction Analysis (2012, methodology): “haviors by Bendixon type of criteria, excluding periodic orbits or forcing convergence to equilibrium sets [17]. Finally we suspect that the density approach to stability analysis proposed by Rantzer [25] is closely connected by duality to the proposed differential framework, and this will also be t”