Third-order nilpotency, nice reachability and asymptotic stability

DOI10.1016/j.jde.2006.10.011zbMath1109.49002OpenAlexW2129324915MaRDI QIDQ863924

Michael Margaliot, Yoav Sharon

Publication date: 12 February 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.10.011

zbMATH Keywords

optimal controlglobal asymptotic stabilityLie bracketsingular controlChen seriesarbitrary switchingnonlinear switched systemsP. Hall basisbang--bang controlfirst- and second-order maximum principleSussmann's product expansion

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Operator-theoretic methods (93B28) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Existence theories for optimal control problems involving ordinary differential equations (49J15) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (15)

On the analysis of nonlinear nilpotent switched systems using the Hall-Sussmann system ⋮ Stability analysis of switched systems using variational principles: An introduction ⋮ Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings ⋮ On robust Lie-algebraic stability conditions for switched linear systems ⋮ The integer approximation error in mixed-integer optimal control ⋮ Combinatorial integral approximation ⋮ Explicit construction of a Barabanov norm for a class of positive planar discrete-time linear switched systems ⋮ Controllability of Boolean control networks via the Perron-Frobenius theory ⋮ Robustness under control sampling of reachability in fixed time for nonlinear control systems ⋮ On stabilization of switched linear systems ⋮ A simplification of the Agrachev-Gamkrelidze second-order variation for bang-bang controls ⋮ A second-order maximum principle for discrete-time bilinear control systems with applications to discrete-time linear switched systems ⋮ Root-mean-square gains of switched linear systems: a variational approach ⋮ On the discretization of switched linear systems ⋮ High-order maximum principles for the stability analysis of positive bilinear control systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability analysis of switched systems using variational principles: An introduction
• Control systems which generate decomposable Lie algebras
• Stability of switched systems: a Lie-algebraic condition
• Theory of chattering control with applications to astronautics, robotics, economics, and engineering
• Switching in systems and control
• The problem of absolute stability: A dynamic programming approach
• Control theory from the geometric viewpoint.
• Stability of discrete linear inclusion
• Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions
• A condition for the stability of switched nonlinear systems
• Lie-Algebraic Stability Criteria for Switched Systems
• A High Order Test for Optimality of Bang–Bang Controls
• Nilpotent and High-Order Approximations of Vector Field Systems
• A Bang-Bang Theorem with Bounds on the Number of Switchings
• Discrete and Continuous Bang-Bang and Facial Spaces Or: Look for the Extreme Points
• The High Order Maximal Principle and Its Application to Singular Extremals
• Linear Matrix Inequalities in System and Control Theory
• Stability Analysis of Second-Order Switched Homogeneous Systems
• On the Local Structure of Optimal Trajectories in R³
• Basic problems in stability and design of switched systems
• Necessary and sufficient conditions for absolute stability: the case of second-order systems
• The “Bang-Bang” Problem for Certain Control Systems in $GL(n,R)$
• Chronological algebras: combinatorics and control

This page was built for publication: Third-order nilpotency, nice reachability and asymptotic stability