Synthesis of a Stable Discrete-Time Repetitive Controller for MIMO Systems

1995 ◽  
Vol 117 (1) ◽  
pp. 92-98 ◽  
Author(s):  
Nader Sadegh
Keyword(s):  
Discrete Time ◽  
Mimo Systems ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Linear Time Invariant ◽  
Closed Loop Systems ◽  
Necessary And Sufficient ◽  
Time Invariant ◽  
Flexible Mechanical System

This paper presents some new results on synthesis and stability analysis of a class of repetitive controllers for discrete-time multi-input multi-output (MIMO) linear time-invariant (LTI) systems. In particular, the necessary and sufficient conditions for exponential stability of the resulting closed-loop systems are derived. A simulation case study featuring a flexible mechanical system is also presented.

Fractional-order linear time invariant swarm systems: asymptotic swarm stability and time response analysis

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Mojtaba Soorki ◽  
Mohammad Tavazoei
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Time Response ◽  
Response Analysis ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Response Analysis ◽  
Necessary And Sufficient ◽  
Time Invariant

AbstractThis paper deals with fractional-order linear time invariant swarm systems. Necessary and sufficient conditions for asymptotic swarm stability of these systems are presented. Also, based on a time response analysis the speed of convergence in an asymptotically swarm stable fractional-order linear time invariant swarm system is investigated and compared with that of its integer-order counterpart. Numerical simulation results are presented to show the effectiveness of the paper results.

scholarly journals Controllability of networked higher-dimensional systems with one-dimensional communication

2017 ◽  
Vol 375 (2088) ◽  
pp. 20160215 ◽  
Author(s):  
Lin Wang ◽  
Xiaofan Wang ◽  
Guanrong Chen
Keyword(s):  
Network Topology ◽  
Linear Time ◽  
Sufficient Conditions ◽  
External Control ◽  
One Dimensional ◽  
Networked System ◽  
Linear Time Invariant ◽  
Higher Dimensional ◽  
Necessary And Sufficient ◽  
Time Invariant

In this paper, the state controllability of networked higher-dimensional linear time-invariant dynamical systems is considered, where communications are performed through one-dimensional connections. The influences on the controllability of such a networked system are investigated, which come from a combination of network topology, node-system dynamics, external control inputs and inner interactions. Particularly, necessary and sufficient conditions are presented for the controllability of the network with a general topology, as well as for some special settings such as cycles and chains, which show that the observability of the node system is necessary in general and the controllability of the node system is necessary for chains but not necessary for cycles. Moreover, two examples are constructed to illustrate that uncontrollable node systems can be assembled to a controllable networked system, while controllable node systems may lead to uncontrollable systems even for the cycle topology. This article is part of the themed issue ‘Horizons of cybernetical physics’.

DISSIPATIVE DYNAMICAL SYSTEMS IN A BEHAVIORAL CONTEXT

1991 ◽  
Vol 01 (01) ◽  
pp. 1-25 ◽  
Author(s):  
SIEP WEILAND ◽  
JAN C. WILLEMS
Keyword(s):  
Dynamical Systems ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Dissipative System ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Dissipative Dynamical Systems ◽  
Necessary And Sufficient ◽  
Lq Theory ◽  
Time Invariant

Various conceptual definitions of dissipativeness of time invariant dynamical systems are introduced. A formal distinction is made between external and internal dissipativeness and it is shown that, under certain conditions, these notions are equivalent. A characterization of the class of internal storage functions associated with a dissipative system is given. The results are applied to the class of finite-dimensional linear time invariant systems. Necessary and sufficient conditions for dissipativeness of systems in this class are derived and the relation to LQ-theory is discussed.

scholarly journals Stability analysis of periodically switched linear systems using Floquet theory

2004 ◽  
Vol 2004 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Cevat Gökçek
Keyword(s):  
Exponential Stability ◽  
Floquet Theory ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Linear Time Invariant ◽  
Fast Switching ◽  
Switching Rule ◽  
Necessary And Sufficient ◽  
Time Invariant

Stability of a switched system that consists of a set of linear time invariant subsystems and a periodic switching rule is investigated. Based on the Floquet theory, necessary and sufficient conditions are given for exponential stability. It is shown that there exists a slow switching rule that achieves exponential stability if at least one of these subsystems is asymptotically stable. It is also shown that there exists a fast switching rule that achieves exponential stability if the average of these subsystems is asymptotically stable. The results are illustrated by examples.

scholarly journals Swarm Stability Analysis of High-Order Linear Time-Invariant Singular Multiagent Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Mingyu Fu ◽  
Shimin Wang ◽  
Yirui Cong
Keyword(s):  
Multiagent Systems ◽  
Stability Problem ◽  
Linear Time ◽  
Sufficient Conditions ◽  
High Order ◽  
Graph Topology ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Necessary And Sufficient ◽  
Time Invariant

The swarm stability problem of high-order linear time-invariant (LTI) singular multiagent systems with directed graph topology is investigated extensively. Consensus of multiagent systems can be regarded as a specific case of swarm stability problem. Necessary and sufficient conditions for both swarm stability and consensus are presented. These conditions depend on the graph topology and generalized inverse theory, the dynamics of agents, and interaction among the neighbours. Several examples to illustrate the effectiveness of theoretical results are given.

scholarly journals Simultaneous exact model matching with stability by output feedback

2017 ◽  
Vol 68 (2) ◽  
pp. 148-152
Author(s):  
Konstadinos H. Kiritsis
Keyword(s):  
Output Feedback ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Dynamic Output Feedback ◽  
Model Matching ◽  
Linear Time Invariant ◽  
Exact Model ◽  
Linear Time Invariant Systems ◽  
Necessary And Sufficient ◽  
Time Invariant

Abstract In this paper, is studied the problem of simultaneous exact model matching by dynamic output feedback for square and invertible linear time invariant systems. In particular, explicit necessary and sufficient conditions are established which guarantee the solvability of the problem with stability and a procedure is given for the computation of dynamic controller which solves the problem.

scholarly journals Reliable disturbance rejection

2005 ◽  
Vol 16 (1) ◽  
pp. 56-59
Author(s):  
Pedro M. G. Ferreira
Keyword(s):  
General Problem ◽  
Disturbance Rejection ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Factorization Approach ◽  
Linear Time Invariant ◽  
Actuator Failures ◽  
Linear Time Invariant Systems ◽  
Necessary And Sufficient ◽  
Time Invariant

The paper studies the reliability (sensor and actuator failures) of the asymptotic disturbance rejection problem for linear time invariant systems using the factorization approach, assuming that not all loops fail simultaneously and that sensor and actuator do not fail simultaneously. The plant is two-output, i.e. two-vector-output, and the disturbance is at the measured output of the plant. Necessary and sufficient conditions are presented for the general problem and a simple solution is given for problems with stable plants.

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