Equivalent Time-invariant System Research Articles

Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions

In this article, we present a stability analysis of linear time-invariant systems in control theory. The linear time-invariant systems under consideration involve the diagonal norm bounded linear differential inclusions. We propose a methodology based on low-rank ordinary differential equations. We construct an equivalent time-invariant system (linear) and use it to acquire an optimization problem whose solutions are given in terms of a system of differential equations. An iterative method is then used to solve the system of differential equations. The stability of linear time-invariant systems with diagonal norm bounded differential inclusion is studied by analyzing the Spectrum of equivalent systems.

Stability, Noise, and Nonlinear Distortion Analysis of a Sampling OPLL

The behavior of a sampling optical phase-locked loop (OPLL) is analyzed. An equivalent time invariant system model for the sampling OPLL was derived. With the help of the model, the stability of a sampling OPLL was found to depend not only on the sampling frequency but also on the duty cycle of the sampling pulse. In addition, the closed-form solutions for the sampling OPLL output noise and nonlinear distortions were also derived. The theoretical results were validated by numeric simulations.

Mean Square Stability of Model Based Networked Control Systems with Multiplicative Noise

This paper presents a necessary and sufficient condition of mean square stability of a model based networked control systems (MB-NCS) with multiplicative noise, where a linear discrete time plant is controlled by using a model state feedback. The lifting approach is employed, and the original time varying system is recast as an equivalent time invariant system whose mean square stability is investigated. The necessary and sufficient condition derived here is given as a set of a linear matrix inequality and linear equations, which enjoys an advantage on numerical computation.

New Results on Stability and Stabilization of Networked Control Systems With Short Time-Varying Delay.

New stability criteria and stabilization methods on networked control systems (NCSs) with short time-varying delay (STVD) are proposed in this paper. An NCS with STVD is transformed into a time-varying discrete time system. And then, this discrete time system is converted into a equivalent time-invariant system with norm-bounded uncertainties by using robust control techniques. Using this method, the conservatism of the stability condition caused by STVD can be reduced. Based on that, a single norm-bounded uncertainty is replaced by N norm-bounded uncertainties to further reduce conservatism. Theoretical analysis shows that when N is increased, the stability condition becomes less conservative. For a fixed sampling period, the obtained stability conditions explicitly depend on the upper and lower bounds of the time delay. The existence condition and design method for the controllers are also presented. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed scheme.

Dynamic analysis of a geared rotor system considering a slant crack on the shaft

The vibration problems associated with geared systems have been the focus of research in recent years. As the torque is mainly transmitted by the geared system, a slant crack is more likely to appear on the gear shaft. Due to the slant crack and its breathing mechanism, the dynamic behavior of cracked geared system would differ distinctly with that of uncracked system. Relatively less work is reported on slant crack in the geared rotor system during the past research. Thus, the dynamic analysis of a geared rotor-bearing system with a breathing slant crack is performed in the paper. The finite element model of a geared rotor with slant crack is presented. Based on fracture mechanics, the flexibility matrix for the slant crack is derived that accounts for the additional stress intensity factors. Three methods for whirling analysis, parametric instability analysis and steady-state response analysis are introduced. Then, by taking a widely used one-stage geared rotor-bearing system as an example, the whirling frequencies of the equivalent time-invariant system, two types of instability regions and steady-state response under the excitations of unbalance forces and tooth transmission errors, are computed numerically. The effects of crack depth, position and type (transverse or slant) on the system dynamic behaviors are considered in the discussion. The comparative study with slant cracked geared rotor is carried out to explore distinctive features in their modal, parametric instability and frequency response behaviors.

Time-invariant representation of discrete periodic systems

A large number of results from linear time-invariant system theory can be extended to periodic systems provided an equivalent time-invariant system can be found. This paper presents a simple and numerically reliable procedure to achieve the same. It is shown that, using a stacked representation of periodic systems, under system equivalence, a minimal-order generalized state-space description can always be obtained.

Stability Conditions Derived from Spectral Theory: Discrete Systems with Periodic Feedback

By use of the spectral theory of linear operators, necessary and sufficient conditions are derived for the stability of a class of discrete time feedback systems with a periodically time-varying feedback gain. These conditions involve a Nyquist plot for an equivalent time-invariant system which may be determined from the frequency response function of the system under consideration. In the special case of a scalar-input scalar-output system, these conditions may be given in a particularly simple form.