Related Experiment Videos

Passivity and Passification for a Class of Uncertain Switched Stochastic Time-Delay Systems

Jie Lian, Peng Shi, Zhi Feng

    IEEE Transactions on Cybernetics
    |June 6, 2012
    PubMed

    Related Concept Videos

    Classification of Systems-II01:31

    Classification 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,
    State Space Representation01:27

    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...
    Second Order systems II01:18

    Second Order systems II

    In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
    If  ζ...
    Classification of Systems-I01:26

    Classification of Systems-I

    Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
    Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
    Linear time-invariant Systems01:23

    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...
    Time and frequency -Domain Interpretation of Phase-lag Control01:21

    Time and frequency -Domain Interpretation of Phase-lag Control

    Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
    Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...