Input-to-State Stability analysis for interconnected difference equations with delay

DOI10.1007/s00498-012-0080-4zbMath1238.93096OpenAlexW2121215794MaRDI QIDQ422409

Mircea Lazar, Andrew R. Teel, Rob H. Gielen

Publication date: 16 May 2012

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00498-012-0080-4

zbMATH Keywords

time delaylarge-scale systemsdifference equationsLyapunov methodssmall-gain theorem

Mathematics Subject Classification ID

Discrete-time control/observation systems (93C55) Input-output approaches in control theory (93D25)

Related Items

Discrete Razumikhin-type stability theorems for stochastic discrete-time delay systems, Input-to-state stability for time-varying delayed systems in Halanay-type inequality forms, Exponential input-to-state stability under events for hybrid dynamical networks with coupling time-delays, Semiglobal practical integral input-to-state stability for a family of parameterized discrete-time interconnected systems with application to sampled-data control systems, Compensation of time-varying input delay for discrete-time nonlinear systems, Event-triggered control for discrete-time delay systems

Cites Work

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• Equivalence between the Lyapunov-Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems
• A small-gain condition for iISS of interconnected retarded systems based on Lyapunov-Krasovskii functionals
• Stabilization of polytopic delay difference inclusions via the razumikhin approach
• Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties
• Input-output analysis of large-scale interconnected systems. Decomposition, well-posedness and stability
• Input-to-state stability for discrete time-delay systems via the Razumikhin technique
• Dissipative dynamical systems. I: General theory
• Razumikhin-type stability theorems for discrete delay systems
• Lyapunov Methods for Time-Invariant Delay Difference Inclusions
• Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions
• A vector small-gain theorem for general non-linear control systems
• Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem
• A nonlinear small gain theorem for the analysis of control systems with saturation
• A Multichannel IOS Small Gain Theorem for Systems With Multiple Time-Varying Communication Delays
• Comments on "A Multichannel IOS Small Gain Theorem for Systems With Multiple Time-Varying Communication Delays
• Discrete-time Lyapunov-based small-gain theorem for parameterized interconnected ISS systems
• Decentralized MPC of nonlinear systems: An input‐to‐state stability approach
• Stability of time-delay systems
• Input-to-state stability for discrete-time nonlinear systems