Related Experiment Video
Updated: May 27, 2026
11:06
A Human-machine-interface Integrating Low-cost Sensors with a Neuromuscular Electrical Stimulation System for Post-stroke Balance Rehabilitation
Published on: April 12, 2016
Partial stabilization of uncertain nonlinear systems.
1School of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Blvd., P.O. Box 71555/313, Shiraz, Iran. binazadeh@sutech.ac.ir
ISA Transactions
|November 9, 2011
Summary
This study introduces two methods for robust partial stabilization of uncertain nonlinear systems by dividing them into subsystems. A novel partial sliding mode control and a Lyapunov-based approach ensure stability of specific system states despite uncertainties.
Area of Science:
- Control Theory
- Nonlinear Systems
- Robust Control
Background:
- Partial stabilization is crucial for complex nonlinear systems.
- Uncertainties in system dynamics pose significant challenges.
- Existing methods may not adequately address robust partial stabilization.
Purpose of the Study:
- To present two novel approaches for robust partial stabilization of uncertain nonlinear systems.
- To design controllers that stabilize specific subsystems while maintaining robustness.
- To investigate the efficacy of sliding mode and Lyapunov-based control for partial stabilization.
Main Methods:
- System decomposition into two subsystems based on stability requirements.
- Design of a reduced input vector for asymptotic stabilization of the first subsystem.
- Development of a partial sliding mode control technique using a specifically designed sliding surface.
- Application of a Lyapunov-based controller augmented with additional feedback for robustness.
Main Results:
- The partial sliding mode method guarantees stability of the first subsystem.
- The Lyapunov-based approach with additional feedback ensures robust partial stabilization.
- Both methods effectively address partial stabilization in the presence of system uncertainties.
Conclusions:
- The proposed methods offer effective solutions for robust partial stabilization of uncertain nonlinear systems.
- Partial sliding mode control provides a new avenue for targeted state stability.
- Lyapunov-based control combined with feedback enhances robustness against system uncertainties.
Related Concept Videos
01:21Linear Approximation in Time Domain
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
01:16Statically Indeterminate Problem Solving
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
01:24Pole and System Stability
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
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...
01:24BIBO 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.
01:26Linear Approximation in Frequency Domain
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.