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State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

State Space to Transfer Function

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for k_a Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...

Transfer Function to State Space

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...

BIBO stability of continuous and discrete -time systems

BIBO 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....

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

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Related Experiment Video

Updated: Aug 27, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Observability Decomposition-Based Decentralized Kalman Filter and Its Application to Resilient State Estimation under

¹School of Intelligent Mechatronics Engineering, Sejong University, Seoul 05006, Korea.

Sensors (Basel, Switzerland)

|September 23, 2022

Summary

This study introduces an optimal decentralized Kalman filter for linear systems with Gaussian noise. It enhances resilience against sparse sensor attacks using a novel detection and estimation algorithm for improved state estimation accuracy.

Keywords:

attack resilience decentralized Kalman filter information fusion observability decomposition redundant observability secure state estimation sparse sensor attack

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Last Updated: Aug 27, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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Published on: October 28, 2022

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A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

Area of Science:

Control Systems Engineering
Signal Processing
Cyber-Physical Systems Security

Background:

Linear time-invariant systems are susceptible to Gaussian noise and sensor attacks.
Decentralized Kalman filtering offers advantages in distributed systems but requires robust attack mitigation.

Purpose of the Study:

To develop an optimal decentralized Kalman filter for discrete-time linear systems.
To design a resilient state estimation algorithm effective against sparse sensor attacks and Gaussian noise.

Main Methods:

Observability decomposition for decentralized Kalman filter design.
Chi-squared (χ2) test for sensor attack detection.
Maximum likelihood decision rule for resilient state estimation under attack.

Main Results:

The proposed filter achieves minimum variance state estimation in the absence of attacks.
The attack detection and resilient estimation scheme effectively handles sparse sensor attacks.
Simulations confirm the algorithm's effectiveness on a motor-controlled torsion system.

Conclusions:

The developed decentralized Kalman filter provides optimal state estimation under Gaussian disturbances.
The integrated attack detection and resilient estimation ensures secure and accurate state estimation in compromised environments.