Related Experiment Video
Updated: Jan 9, 2026
08:18
WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
Published on: August 15, 2020
5.4K
Analysis and Control of Semi-Markov Jump Linear Systems Under Persistent Disturbances via Full Utilization of
IEEE Transactions on Cybernetics
|December 3, 2025
Summary
This study addresses stability and control for discrete-time semi-Markov jump systems (SMJSs) with incomplete information. New methods leverage all known data and approximate missing parts for enhanced system performance and boundedness.
Area of Science:
- Control Systems Engineering
- Stochastic Systems Analysis
- Applied Mathematics
Background:
- Discrete-time semi-Markov jump systems (SMJSs) present challenges due to potentially fragmentary semi-Markov kernel (SMK) information.
- Incomplete statistical characterization of stochastic processes necessitates robust analysis and control methods.
Purpose of the Study:
- To develop novel approaches for analyzing stability, boundedness, and stabilizing control of SMJSs with fragmentary SMK.
- To enhance the utilization of available SMK information and incorporate approximated unknown SMK data.
Main Methods:
- Proposed new criteria for stability and control by leveraging all known SMK information.
- Introduced a polytopic approach to approximate unknown SMK information.
- Constructed a polytopic quadratic Lyapunov-like function (LF) for improved feasibility.
Main Results:
- Derived new criteria for stability and control, enhancing feasibility compared to existing methods.
- Ensured ultimate boundedness of the closed-loop SMJLS in the mean-square sense.
- Demonstrated improved performance by incorporating both known and approximated SMK information.
Conclusions:
- The proposed methods effectively handle fragmentary SMK information in SMJSs.
- The polytopic approximation and LF enhance the feasibility of analysis and control design.
- The approach is validated through numerical and simulated chemical process examples.
Related Concept Videos
01:23Linear time-invariant Systems
846
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...
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...
846
01:24BIBO stability of continuous and discrete -time systems
871
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....
871
01:26Feedback control systems
663
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
663
01:21Linear Approximation in Time Domain
323
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,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
323
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
271
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
271
01:22Multi-input and Multi-variable systems
373
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
In the absence of...
373