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This paper presents necessary and sufficient conditions to achieve consensus for a homogeneous network of linear second-order systems. Simple controllers to achieve consensus with a guaranteed rate of convergence are proposed. The only requirement is that the network graph contain a spanning tree. The eigenvalues of the graph Laplacian can be complex and the consensus behavior of the systems will...
We study the problem of stabilizing a switched linear system with disturbance using sampled and quantized measurements of its state. The switching is assumed to be slow in the sense of combined dwell-time and average dwell-time, while the active mode is unknown except at sampling times. Each mode of the switched linear system is assumed to be stabilizable, and the magnitude of the disturbance is constrained...
The design of a nonlinear Luenberger observer for a parametrized linear system is studied. From an observability assumption of the system, the existence of such an observer is concluded. In a second step, a constructive novel algorithm for the identification of multi-input multi-output linear systems is suggested and is implemented on a second order system.
In this work we have proposed a new technique of model order reduction for linear time invariant (LTI) systems with parametric uncertainty. The model order reduction method is based on proper generalized decomposition (PGD). Using PGD, the underlying state variable is expanded as a sum of separated functions of time and uncertain parameters. At first, the stochastic states of the LTI system is represented...
Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability...
This paper addresses the optimal output regulation problem of linear systems with unknown system dynamics. The exogenous signal is presumed to be generated by a continuous-time linear exosystem. Firstly, we formulate the linear optimal output regulation problem (LOORP). Then, we give an offline solution of LOORP to design the optimal static state-feedback servoregulator by solving an algebraic Riccati...
This paper discusses robust iterative learning control (ILC) analysis and synthesis problems that account for model uncertainty in the lifted system representation. In the robust analysis, we transform the robust monotonic convergence condition with unstructured uncertainty into an equivalent convex problem. In this framework, for a given learning gain Q, the design of the learning gain L that maximizes...
In this paper we present a controller that achieves global input-to-state stabilty for a linear system of arbitrary relative degree, subjected to matched and unmatched disturbances. This controller combines the properties of a discontinous term, and a linear one, enforcing a conventional sliding mode using only partial state information. A direct and simple way of choosing the gains for this controller...
We consider the problem of solving a Laplacian system of equations Lx = b in a distributed fashion, where L is the Laplacian of the communication graph. Solving Laplacian systems arises in a number of applications including consensus, distributed control, clock synchronization, localization and calculating effective resistances, to name a few. We leverage our analysis on a randomized variant of Kaczmarz's...
In order to reduce communication in network control systems, it is of great interest to be able to synthesize event-triggered control laws from continuous-time controls. This work proposes a new rule to design event-based stabilizing controllers for linear systems. More precisely, based on a given reference system, a state observer, and a quadratic Lyapunov-like function, an event-based sampling algorithm...
This paper proposes a novel discrete time identification method for flexible wing aircraft models from simulated data. The special properties of the dynamics arise from the fact that all the poles are located very close to the unit circle and their location changes with the flight velocity. Using identification criteria based on Euclidean metrics suffers from the problem of obtaining instability in...
In this paper, the problem of robust set invariance and contractivity with respect to discrete-time dynamical systems is investigated. In contrast to the usual approach consisting in describing regions of system's space by their border surfaces, a dual description of sets in terms of a generator matrix and a, generally nonlinear, generating function is proposed. This leads to the establishment of...
We present in this paper the analysis and the synthesis of robust iterative learning control RILC for linear continuous system based on H∞ approach. The two dimensional 2D systems are studied here to improve the monotonically convergence and to prove the efficiency of the proposed approach. Linear matrix inequality LMI techniques are also used to compute the P type RILC algorithm.
The idea of finding low-rank solutions to matrix or tensor optimization tasks by greedy rank-one methods has been showing itself repeatedly in the literature. The simplest method, and often a central building block in accelerated methods, consists in performing updates along low-rank approximations of the negative gradient. This is convenient as it does increase the rank in a prescribed manner per...
It is well-known that there exist bandlimited signals for which certain sampling series are divergent. One possible way of circumventing the divergence is to adapt the sampling series to the signals. In this paper we study adaptivity in the number of summands that are used in each approximation step, and whether this kind of adaptive signal processing can improve the convergence behavior of the sampling...
In this paper, an observer for Switched Linear Systems (SLS) with unknown inputs is designed. LMI conditions, guaranteeing the asymptotic convergence of the observer derived through multiple Lyapunov functions and LMI region. This is done by decoupling a subset of the system states from the unknown inputs and by estimating the states thanks to a like Luenberger observer. Then, an estimator for the...
In this article, a two-stage iterative algorithm is proposed to improve the convergence of Krylov based iterative methods, typically those of GMRES variants. The principle of the proposed approach is to build an external iteration over the Krylov method, and to frequently store its current residual (at each GMRES restart for instance). After a given number of outer iterations, a least-squares minimization...
The main aim of this paper is to investigate the performance of two iterative methods i.e. Gauss-Seidel (GS) and 2-Point Explicit Group (2-EG) in solving dense linear system associated with the numerical solution of first kind linear Fredholm integral equations. The formulation and implementation of the both methods are presented. In addition, some numerical results are also included to verify the...
A stochastic linear hybrid system is said to be observable if the hybrid state of the system can be uniquely determined from its output. In this paper, we derive conditions for the observability of stochastic linear hybrid systems by exploiting the information obtained from system noise characteristics. Having established the necessary criteria for observability, we study the effect of these conditions...
A primary goal of adaptive observers would be to estimate the true states of a plant. Identification of unknown parameters is of secondary interest and is achieved frequently with the persistent excitation condition of some regressors. Nevertheless, two problems are linked to each other in the classical approaches to adaptive observers; as a result, we get a good state estimate once after a good parameter...
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