Steady-state response of linear time-invariant systems

1966 ◽  
Vol 54 (12) ◽  
pp. 1952-1953 ◽  
Author(s):  
M.L. Liou
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Steady State Response ◽  
Linear Time Invariant ◽  
State Response ◽  
Linear Time Invariant Systems ◽  
Time Invariant

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

scholarly journals Steady-State Response of Periodically Switched Linear Circuits via Augmented Time-Invariant Nodal Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Riccardo Trinchero ◽  
Igor S. Stievano ◽  
Flavio G. Canavero
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Linear Time ◽  
Automatic Generation ◽  
Steady State Response ◽  
Linear Time Invariant ◽  
State Response ◽  
Linear Circuits ◽  
Circuit Components ◽  
Time Invariant

We focus on the simulation of periodically switched linear circuits. The basic notation and theoretical framework are presented, with emphasis on the differences between the linear time-invariant and the time-varying cases. For this important class of circuits and sources defined by periodic signals, the computation of their steady-state response is carried out via the solution of an augmented time-invariant MNA equation in the frequency-domain. The proposed method is based on the expansion of the unknown voltages and currents in terms of Fourier series and on the automatic generation of augmented equivalents of the circuit components. The above equivalents along with the information on circuit topology allow creating, via circuit inspection, a time-invariant MNA equation, the solution of which provides the coefficients of both the time- and the frequency-domain responses of the circuit. Analytical and numerical examples are used to stress the generality and benefits of the proposed approach.

Novel Gaussian State Estimator based on H2 Norm and Steady-State Variance

2020 ◽  
Author(s):  
Alesi Augusto De Paula ◽  
Víctor Costa da Silva Campos ◽  
Guilherme Vianna Raffo ◽  
Bruno Otávio Soares Teixeira
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Estimation Error ◽  
Performance Criterion ◽  
Gaussian State ◽  
State Estimator ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Linear Time Invariant System ◽  
Time Invariant

This paper proposes a novel state estimator for discrete-time linear systems with Gaussian noise. The proposed algorithm is a fixed-gain filter, whose observer structure is more general than Kalman one for linear time-invariant systems. Therefore, the steady-state variance of the estimation error is minimized. For white noise stochastic processes, this performance criterion is reduced to the square H2 norm of a given linear time-invariant system. Then, the proposed algorithm is called observer H2 filter (OH2F). This is the standard Wiener-Hopf or Kalman-Bucy filtering problem. As the Kalman predictor and Kalman filter are well-known solutions for such a problem, they are revisited.

scholarly journals Efficient Model Predictive Algorithms for Tracking of Periodic Signals

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yun-Chung Chu ◽  
Michael Z. Q. Chen
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Operating Point ◽  
Quadratic Program ◽  
Efficient Manner ◽  
Linear Time Invariant ◽  
Predictive Algorithms ◽  
Model Predictive Controllers ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This paper studies the design of efficient model predictive controllers for fast-sampling linear time-invariant systems subject to input constraints to track a set of periodic references. The problem is decomposed into a steady-state subproblem that determines the optimal asymptotic operating point and a transient subproblem that drives the given plant to this operating point. While the transient subproblem is a small-sized quadratic program, the steady-state subproblem can easily involve hundreds of variables and constraints. The decomposition allows these two subproblems of very different computational complexities to be solved in parallel with different sampling rates. Moreover, a receding horizon approach is adopted for the steady-state subproblem to spread the optimization over time in an efficient manner, making its solution possible for fast-sampling systems. Besides the conventional formulation based on the control inputs as variables, a parameterization using a dynamic policy on the inputs is introduced, which further reduces the online computational requirements. Both proposed algorithms possess nice convergence properties, which are also verified with computer simulations.

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