scholarly journals Stationary orbits of linear time-varying observation systems

2021 ◽  
Vol 65 (1) ◽  
pp. 18-24
Author(s):  
A. I. Astrovskii
Keyword(s):  
Vector Function ◽  
Matrix Function ◽  
Transformation Group ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Observation System ◽  
Time Varying ◽  
Observation Systems ◽  
Necessary And Sufficient ◽  
N Vector

In terms of matrix observability, the necessary and sufficient conditions are obtained for the linear timevarying observation system to have stationary orbits with respect to the linear time-varying transformation group of class C1 . The full invariant of the action of a transformation group is described. It is proved that for any matrix function A c C(T, Rn×n ), there exists such an n-vector function c(t), t c T, that the pair (A, c) is uniformly observable. The algorithm for constructing a stationary system is described.

Necessary and Sufficient Conditions for Assignability of the Lyapunov Spectrum of Discrete Linear Time-Varying Systems

2018 ◽  
Vol 63 (11) ◽  
pp. 3825-3837 ◽  
Author(s):  
Artur Babiarz ◽  
Irina Banshchikova ◽  
Adam Czornik ◽  
Evgenii K. Makarov ◽  
Michal Niezabitowski ◽  
...  
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lyapunov Spectrum ◽  
Time Varying ◽  
Time Varying Systems ◽  
Necessary And Sufficient

scholarly journals Inverse Commutativity Conditions for Second-Order Linear Time-Varying Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Mehmet Emir Koksal
Keyword(s):  
Differential Equation ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Time Varying ◽  
Order Linear ◽  
Time Varying Systems ◽  
Initial States ◽  
Necessary And Sufficient

The necessary and sufficient conditions where a second-order linear time-varying system A is commutative with another system B of the same type have been given in the literature for both zero initial states and nonzero initial states. These conditions are mainly expressed in terms of the coefficients of the differential equation describing system A. In this contribution, the inverse conditions expressed in terms of the coefficients of the differential equation describing system B have been derived and shown to be of the same form of the original equations appearing in the literature.

On the Reducibility of the Discrete Linear Time-Varying Systems

2015 ◽  
Vol 789-790 ◽  
pp. 1027-1033
Author(s):  
Jerzy Klamka ◽  
Elżbieta Ferenstein ◽  
Artur Babiarz ◽  
Michał Niezabitowski
Keyword(s):  
Lyapunov Exponents ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Time Varying ◽  
Identity Matrix ◽  
Original Result ◽  
Time Varying Systems ◽  
Basic Facts ◽  
Necessary And Sufficient

For the discrete linear time-varying systems we present basic facts and definitions concerning the Lyapunov transformation, kinematic similarity and reducibility in the context of stability and Lyapunov exponents theory. Moreover, the paper contains the original result giving the necessary and sufficient conditions for the reducibility of a system to system with identity matrix.

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.

Coupled Stability of Multiport Systems—Theory and Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 419-428 ◽  
Author(s):  
J. E. Colgate
Keyword(s):  
Stability Property ◽  
Force Feedback ◽  
Linear Time ◽  
Experimental Studies ◽  
Sufficient Conditions ◽  
Direct Drive ◽  
Property A ◽  
Linear Time Invariant ◽  
The Stability ◽  
Necessary And Sufficient

This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

Sign in / Sign up

Export Citation Format

Share Document