Non-smooth and time-varying systems of geometrically nonlinear beams

Abstract This paper addresses a finite-time regulation problem for time-varying nonlinear systems in p-normal form. This class of time-varying systems includes a well-known lower-triangular system and a chain of power integrator systems as special cases. No growth condition on time-varying uncertainties is imposed. The control law can guarantee that all closed-loop trajectories are bounded and well defined. Furthermore, all states converge to zero in finite time.

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Energy-to-Peak Output Tracking Control of Actuator Saturated Periodic Piecewise Time-Varying Systems With Nonlinear Perturbations

IEEE Transactions on Systems Man and Cybernetics Systems ◽

10.1109/tsmc.2021.3049524 ◽

2021 ◽

pp. 1-13

Author(s):

Xiaochen Xie ◽

James Lam ◽

Chenchen Fan ◽

Xiaomei Wang ◽

Ka-Wai Kwok

Keyword(s):

Tracking Control ◽

Time Varying ◽

Nonlinear Perturbations ◽

Output Tracking ◽

Output Tracking Control ◽

Time Varying Systems

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The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽

10.3390/eng2010008 ◽

2021 ◽

Vol 2 (1) ◽

pp. 99-125

Author(s):

Edward W. Kamen

Keyword(s):

Discrete Time ◽

Initial Conditions ◽

Linear Time ◽

Order Term ◽

Initial Time ◽

Time Varying ◽

Varying Coefficients ◽

Time Signals ◽

Time Varying Systems ◽

Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

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