Related Experiment Video
Updated: Jun 25, 2026
10:45
Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays
Published on: May 29, 2017
Stability of Time-Varying Impulsive Systems With State-Dependent Delay and Its Application in Complex Networks
Summary
This study analyzes the stability of complex impulsive systems with state-dependent delay (SDD). New Lyapunov-based criteria reveal how these systems maintain stability despite time-varying parameters and impulsive effects.
Area of Science:
- Dynamical Systems and Control Theory
- Nonlinear Systems Analysis
- Network Synchronization
Background:
- Impulsive systems with time-varying parameters and state-dependent delay (SDD) present significant analytical challenges due to strong nonlinear coupling.
- Existing stability analysis methods are often insufficient for systems exhibiting these combined complex dynamics.
Purpose of the Study:
- To investigate and establish sufficient conditions for the stability of time-varying impulsive systems with state-dependent delay (SDD).
- To extend these stability findings to address the synchronization problem in complex networks with impulsive disturbances.
Main Methods:
- Development of novel Lyapunov-based stability criteria tailored for systems with time-varying parameters, impulsive effects, and state-dependent delay (SDD).
- Analysis of the interaction mechanisms between continuous dynamics, impulsive perturbations, and the state-dependent delay term.
Main Results:
- Several sufficient conditions are derived to guarantee the stability of the investigated systems.
- The proposed criteria effectively characterize the systems' inherent robustness against impulsive perturbations.
- The stability criteria are successfully extended to solve the synchronization problem for complex networks with impulsive disturbances.
Conclusions:
- The study provides effective analytical tools for understanding the stability of complex impulsive systems with state-dependent delay (SDD).
- The derived criteria offer insights into the robustness of these systems and their applicability to network synchronization problems.
Related Concept Videos
01:24BIBO stability of continuous and discrete -time systems
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
01:28Stability
The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
01:23Linear time-invariant Systems
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
01:31Classification of Systems-II
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
01:24Transient and Steady-state Response
In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
01:21First Order Systems
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...