scholarly journals Non-exponential Stabilization of Linear Time-invariant Systems by Time-varying Controllers

2011 ◽  
Vol 47 (1) ◽  
pp. 70-78 ◽  
Author(s):  
Masaki INOUE ◽  
Teruyo WADA ◽  
Masao IKEDA
Keyword(s):  
Linear Time ◽  
Exponential Stabilization ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

scholarly journals FE Analysis of Communications Systems for Drive-Thru Restaurants in a Business Dispute Over Specifications and Design Process

2021 ◽  
Vol 38 (1) ◽  
Author(s):  
Robert Peruzzi
Keyword(s):  
Communication System ◽  
Communication Systems ◽  
Linear Time ◽  
Forensic Analysis ◽  
Time Varying ◽  
Audio Quality ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Quick Service ◽  
Time Invariant

Forensic analysis in this case involves the design of a communication system intended for use in Quick Service Restaurant (QSR) drive-thru lanes. This paper provides an overview of QSR communication system components and operation and introduces communication systems and channels. This paper provides an overview of non-linear, time-varying system design as contrasted with linear, time-invariant systems and discusses best design practices. It also provides the details of how audio quality was defined and compared for two potentially competing systems. Conclusions include that one of the systems was clearly inferior to the other — mainly due to not following design techniques that were available at the time of the project.

Linear Approximations for Swing Leg Motion During Gait

1984 ◽  
Vol 106 (2) ◽  
pp. 137-143 ◽  
Author(s):  
W. H. Lee ◽  
J. M. Mansour
Keyword(s):  
Linear Systems ◽  
System Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
State Variables ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Leg Motion ◽  
Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

Active Control of Linear Time-Varying Structures by Confinement of Vibrations

2005 ◽  
Vol 11 (1) ◽  
pp. 89-102 ◽  
Author(s):  
S. Choura ◽  
A. S. Yigit
Keyword(s):  
Control Strategy ◽  
Linear Time ◽  
Steady States ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Slowing Down ◽  
Rapid Removal ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant

We propose a control strategy for the simultaneous suppression and confinement of vibrations in linear time-varying structures. The proposed controller has time-varying gains and can also be used for linear time-invariant systems. The key idea is to alter the original modes by appropriate feedback forces to allow parts of the structure reach their steady states at faster rates. It is demonstrated that the convergence of these parts to zero is improved at the expense of slowing down the settling of the remaining parts to their steady states. The proposed control strategy can be applied for the rapid removal of vibration energy in sensitive parts of a flexible structure for safety or performance reasons. The stability of the closed-loop system is proven through a Lyapunov approach. An illustrative example of a five-link manipulator with a periodic follower force is given to demonstrate the effectiveness of the method for time-varying as well as time-invariant systems.

scholarly journals Exponential Stabilization of Linear Time-Varying Differential Equations with Uncertain Coefficients by Linear Stationary Feedback

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 853
Author(s):  
Vasilii Zaitsev ◽  
Inna Kim
Keyword(s):  
Differential Equation ◽  
Decay Rate ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Time Varying ◽  
Static State ◽  
Linear Time Invariant ◽  
Linear Differential ◽  
Time Invariant

We consider a control system defined by a linear time-varying differential equation of n-th order with uncertain bounded coefficients. The problem of exponential stabilization of the system with an arbitrary given decay rate by linear static state or output feedback with constant gain coefficients is studied. We prove that every system is exponentially stabilizable with any pregiven decay rate by linear time-invariant static state feedback. The proof is based on the Levin’s theorem on sufficient conditions for absolute non-oscillatory stability of solutions to a linear differential equation. We obtain sufficient conditions of exponential stabilization with any pregiven decay rate for a linear differential equation with uncertain bounded coefficients by linear time-invariant static output feedback. Illustrative examples are considered.

scholarly journals Consensus of Noisy Multiagent Systems with Markovian Switching Topologies and Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Multiagent Systems ◽  
Linear Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Graph Properties ◽  
Linear Time Invariant Systems ◽  
Necessary And Sufficient ◽  
Time Invariant

Stochastic multiagent systems have attracted much attention during the past few decades. This paper concerns the continuous-time consensus of a network of agents under directed switching communication topologies governed by a time-homogeneous Markovian process. The agent dynamics are described by linear time-invariant systems, with random noises as well as time-varying delays. Two types of network-induced delays are considered, namely, delays affecting only the output of the agents’ neighbors and delays affecting both the agents’ own output and the output of their neighbors. We present necessary and sufficient consensus conditions for these two classes of multiagent systems, respectively. The design method of consensus gains allows for decoupling the design problem from the graph properties. Numerical simulations are implemented to test the effectiveness of our obtained results as well as the tightness of necessary/sufficient conditions.

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