On Common Linear/Quadratic Lyapunov Functions for Switched Linear Systems

DOI10.1007/978-1-4419-0158-3_25zbMath1184.49029OpenAlexW75345007MaRDI QIDQ5188760

Melania M. Moldovan, M. Seetharama Gowda

Publication date: 5 March 2010

Published in: Nonlinear Analysis and Variational Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4419-0158-3_25

zbMATH Keywords

dualityLyapunov functionscomplementarityswitched linear systems\(\mathbb Z\)-transformations

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Duality theory (optimization) (49N15)

Related Items

H_∞ control for linear switched systems with time‐varying delay and dead‐zone inputs via an adaptive memory controller ⋮ State and dynamic output feedback control of switched linear systems via a mixed time and state-dependent switching law ⋮ A method for determining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation ⋮ Minimum eigenvalue inequalities for \(Z\)-transformations on proper and symmetric cones ⋮ On the bilinearity rank of a proper cone and Lyapunov-like transformations ⋮ A REPRESENTATION THEOREM FOR LYAPUNOV-LIKE TRANSFORMATIONS ON EUCLIDEAN JORDAN ALGEBRAS ⋮ Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time ⋮ Robust fault detection and control for continuous-time switched systems with average dwell time ⋮ Max-type copositive Lyapunov functions for switching positive linear systems ⋮ Dual switched positive systems – a less conservative condition for diagonal quadratic stability

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some P-properties for linear transformations on Euclidean Jordan algebras
• On the existence of a common quadratic Lyapunov function for a rank one difference
• An alternative proof of the Barker, Berman, Plemmons (BBP) result on diagonal stability and extensions
• Z-transformations on proper and symmetric cones
• An iterative method of Lyapunov function construction for differential inclusions
• Stability of switched systems: a Lie-algebraic condition
• On some properties of \(\mathbf P\)-matrix sets
• Switching in systems and control
• Complementarity forms of theorems of Lyapunov and Stein, and related results
• Quasimonotonie und Ungleichungen in halbgeordneten Räumen
• Generalizations of \(\mathbf P_ 0\)- and \(\mathbf P\)-properties; extended vertical and horizontal linear complementarity problems
• The Generalized Order Linear Complementarity Problem
• A common Lyapunov function for stable LTI systems with commuting A-matrices
• On common quadratic Lyapunov functions for stable discrete-time LTI systems
• Some New Results for the Semidefinite Linear Complementarity Problem
• Conditions on the Stability of a Class of Second-Order Switched Systems
• On the Stability of Switched Positive Linear Systems
• On Linear Copositive Lyapunov Functions and the Stability of Switched Positive Linear Systems
• Stability Criteria for Switched and Hybrid Systems
• Cross-Positive Matrices