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Introduction
Published in S. Bingulac, Algorithms for Computer-Aided Design of Multivariable Control Systems, 2018
As in the previous discussion, the D -T model of Eq.(1.30) will be assumed to accurately represent the system at hand. The concept of observability is a fundamental property of systems related to how the measurements, or outputs, interact with the system states. It has been shown that the simple problem of identifying the in itia l state, x(0), by observing a fin ite number of outputs is equivalent to knowing that the complete state information is transmitted to the outputs. Although we know from Eq.(1.32) that the general solution consists of two parts, only the zero-input response need be used to develop the condition under which the in itia l state can be identified from a fin ite number of outputs. The reason for this is that, since the model and inputs are known, the zero-state response could simply be calculated and subtracted away from the total solution.
Vibration Control
Published in Haym Benaroya, Mark Nagurka, Seon Han, Mechanical Vibration, 2017
Haym Benaroya, Mark Nagurka, Seon Han
The concept of observability implies an ability to determine all elements of the state vector of the system from knowledge of the input and output over an arbitrary time interval. Observability depends on the relationship between the state variables and the system output, that is, if measurement of the output allows determination of all the state variables. Since the input is assumed known, observability refers to our ability to determine information about all the modes of the system by monitoring the output. A system is observable if and only if the initial state can be determined from knowledge of the input and output over a finite interval of time.46
Structural Control Theory
Published in You-Lin Xu, Jia He, Smart Civil Structures, 2017
The concept of observability is dual to that of controllability. Observability, as a coupling between the system states and the output, only involves the system matrix A and the output matrix C. Thus, the following observation equation can be considered as () Y=CX
Sensor fault detection and isolation via networked estimation: rank-deficient dynamical systems
Published in International Journal of Control, 2022
M. Doostmohammadian, H. Zarrabi, T. Charalambous
Recall that observability refers to the possibility of reconstructing the entire system states via some state measurements (outputs) over finite time-interval. Denote by the observability Gramian matrix defined as, Having implies that the system (1) is observable by outputs (2) and the states (at every time k) can be obtained by solving the following set of linear algebraic equations on the outputs, Recall that if the conditions (i)–(ii) in Theorem 2.1 hold on the structural system representation, observability Gramian is full-rank for almost all numerical values of the non-zero entries in the system matrix A and output matrix C (Dion et al., 2003; Doostmohammadian & Khan, 2020).
A graph theory approach for regional controllability of Boolean cellular automata
Published in International Journal of Parallel, Emergent and Distributed Systems, 2020
S. Dridi, S. El Yacoubi, F. Bagnoli, A. Fontaine
Control theory is a branch of mathematics that deals with the behaviour of dynamical systems studied in terms of inputs and outputs. With the recent developments in computing, communications, and sensing technologies, the scope of control theory is rapidly evolving to encompass the increasing complexity of real-life phenomena. Controllability and observability are two major concepts of control theory that have been extensively developed during the last two centuries. The concept of controllability refers to the ability of designing control inputs so as to steer the state of the system to desired values within an interval time while the observability describes whether the internal state variables of the system can be externally measured. These concepts are being increasingly useful in a wide range of applications such as biology, biochemistry, biomedical engineering, ecology, economics, etc. [1,2]. Controllable and observable systems have been characterised so far using the Kalman condition in the linear case. The aim of this paper is to find a general way to give a necessary and sufficient condition for controllability of complex systems via cellular automata models. We concentrate in this work on regional controllability via boundary actions on the target region ω that consists in achieving an objective only in a subdomain of the lattice when some specific actions are exerted on the target region boundaries.
Event-triggered bounded consensus for stochastic multi-agent systems with communication delay
Published in International Journal of Control, 2022
Li Li, Zhichen Li, Yuanqing Xia, Jingjing Yan
Controllability of the system reflects the possibility that states of a system can be controlled by external input. Observability reflects the possibility of determining the states by measurement output to reflect internal dynamic characteristics of a system. Only when a system is controllable and observable, can it be possible to design appropriate state feedback controller for realising arbitrarily specified performance. The Assumption 1 is a sufficient condition for the system to be stable.