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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:

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 RLC...

Linear time-invariant Systems

Linear 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...

Linear Approximation in Time Domain

Linear 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...

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.

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Related Experiment Video

Updated: Jul 7, 2026

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

Temporal BYY encoding, Markovian state spaces, and space dimension determination.

¹Dept. of Comput. Sci. and Eng., Chinese Univ. of Hong Kong, China.

IEEE Transactions on Neural Networks

|February 2, 2008

Summary

This study introduces a novel temporal Bayesian Ying-Yang (BYY) learning approach for Markovian state space models. It enhances Hidden Markov Models and linear state spaces with automatic state selection, improving temporal data analysis.

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Area of Science:

Machine Learning
Statistical Modeling
Artificial Intelligence

Background:

Current temporal coding approaches often overlook state space dynamics.
Markovian models are crucial for sequential data but face challenges in state determination.
Bayesian Ying-Yang (BYY) learning offers a unique framework for probabilistic modeling.

Purpose of the Study:

To develop a novel temporal Bayesian Ying-Yang (BYY) learning framework for Markovian state space models.
To extend existing discrete (Hidden Markov Model) and continuous (linear state space) models.
To introduce a new adaptive learning mechanism for automatic state number or dimension selection.

Main Methods:

Utilizing temporal Bayesian Ying-Yang (BYY) learning principles.
Developing extensions for discrete state Hidden Markov Models.
Developing extensions for continuous state linear state spaces.
Implementing a new learning mechanism for automatic model order selection.

Main Results:

New insights and results for both discrete and continuous state space models.
Demonstration of a learning mechanism that automatically selects the number of states or state space dimension.
Experimental validation of the proposed approach's efficacy.

Conclusions:

The temporal BYY learning framework provides a powerful and flexible approach to Markovian state space modeling.
The proposed automatic state selection mechanism enhances model adaptability and reduces manual tuning.
This work offers significant advancements in temporal data analysis and probabilistic modeling.