124 research outputs found
Constructive necessary and sufficient condition for the stability of quasi-periodic linear impulsive systems
International audienceThe paper provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions are assumed to occur quasi-periodically. Based on the set-theoretic conditions for robust stability of uncertain linear systems, the existence of polyhedral Lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi-periodic linear impulsive systems. A constructive method is developed for testing the stability of the system and for computing set-induced polyhedral Lyapunov functions. The method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete-time parametric uncertain systems with the state matrix belonging to a convex polytopic set
<i>H</i><sub>2</sub> and mixed <i>H</i><sub>2</sub>/<i>H</i><sub>∞</sub> Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes
Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation
Homogeneous Polynomial Lyapunov Functions for Robust Local Synchronisation with Time-varying Uncertainties
This study studies robust local synchronisation in multi-agent systems with time-varying parametric uncertainties constrained in a polytope. In contrast to the existing methods with non-convex conditions via using quadratic Lyapunov function, a new criteria is proposed based on using homogeneous polynomial Lyapunov functions where the original system is suitably approximated by an uncertain polytopic system. Furthermore, the corresponding tractable conditions of linear matrix inequalities have been provided by exploiting the squares matrix representation. Then, the polytopic synchronisation margin problem is, for the first time, proposed and investigated via handling generalised eigenvalue problems. Lastly, numerical examples illustrate the usefulness of the proposed method.postprin
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
LMI-Based Reset Unknown Input Observer for State Estimation of Linear Uncertain Systems
This paper proposes a novel kind of Unknown Input Observer (UIO) called Reset
Unknown Input Observer (R-UIO) for state estimation of linear systems in the
presence of disturbance using Linear Matrix Inequality (LMI) techniques. In
R-UIO, the states of the observer are reset to the after-reset value based on
an appropriate reset law in order to decrease the norm and settling time
of estimation error. It is shown that the application of the reset theory to
the UIOs in the LTI framework can significantly improve the transient response
of the observer. Moreover, the devised approach can be applied to both SISO and
MIMO systems. Furthermore, the stability and convergence analysis of the
devised R-UIO is addressed. Finally, the efficiency of the proposed method is
demonstrated by simulation results
Robust L2 - L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process
This paper investigates the problem of robust L2 - L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process. The time-varying transition probabilities which evolve as a nonhomogeneous jump process are described by a polytope, and parameter-dependent and mode-dependent Lyapunov function is constructed for such system, and then a robust L2 -L8 filter is designed which guarantees that the resulting error dynamic system is robustly stochasticallystable and satisfies a prescribed L2 - L∞ performance index. A numerical example is given to illustrate the effectiveness of the developed techniques
Networked control systems in the presence of scheduling protocols and communication delays
This paper develops the time-delay approach to Networked Control Systems
(NCSs) in the presence of variable transmission delays, sampling intervals and
communication constraints. The system sensor nodes are supposed to be
distributed over a network. Due to communication constraints only one node
output is transmitted through the communication channel at once. The scheduling
of sensor information towards the controller is ruled by a weighted
Try-Once-Discard (TOD) or by Round-Robin (RR) protocols. Differently from the
existing results on NCSs in the presence of scheduling protocols (in the
frameworks of hybrid and discrete-time systems), we allow the communication
delays to be greater than the sampling intervals. A novel hybrid system model
for the closed-loop system is presented that contains {\it time-varying delays
in the continuous dynamics and in the reset conditions}. A new
Lyapunov-Krasovskii method, which is based on discontinuous in time Lyapunov
functionals is introduced for the stability analysis of the delayed hybrid
systems. Polytopic type uncertainties in the system model can be easily
included in the analysis. The efficiency of the time-delay approach is
illustrated on the examples of uncertain cart-pendulum and of batch reactor
On delayed genetic regulatory networks with polytopic uncertainties: Robust stability analysis
Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results
A new robust kalman filter algorithm under outliers and system uncertainties
This paper proposes a new robust Kalman filter algorithm under outliers and system uncertainties. The robust Kalman filter of Durovic and Kovacevic is extended to include unknown-but-bounded parameter uncertainties in the state or observation matrix. We first formulate the robust state estimation problem as an M-estimation problem, which leads to an unconstrained nonlinear optimization problem. This is then linearized and solved iteratively as a series of linear least-squares problem. These least-squares problems, subject to the bounded system uncertainties using the robust least squares method proposed by A. Ben-Tal and A. Nemirovski. Simulation results show that the new algorithm leads to a better performance than the conventional algorithms under outliers as well as system uncertainties. © 2005 IEEE.published_or_final_versio
Virtual Structures Based Autonomous Formation Flying Control for Small Satellites
Many space organizations have a growing need to fly several small satellites close together in order to collect and correlate data from different satellite sensors. To do this requires teams of engineers monitoring the satellites orbits and planning maneuvers for the satellites every time the satellite leaves its desired trajectory or formation. This task of maintaining the satellites orbits quickly becomes an arduous and expensive feat for satellite operations centers. This research develops and analyzes algorithms that allow satellites to autonomously control their orbit and formation without human intervention. This goal is accomplished by developing and evaluating a decentralized, optimization-based control that can be used for autonomous formation flight of small satellites. To do this, virtual structures, model predictive control, and switching surfaces are used. An optimized guidance trajectory is also develop to reduce fuel usage of the system. The Hill-Clohessy-Wiltshire equations and the D\u27Amico relative orbital elements are used to describe the relative motion of the satellites. And a performance comparison of the L1, L2, and L∞ norms is completed as part of this work. The virtual structure, MPC based framework combined with the switching surfaces enables a scalable method that allows satellites to maneuver safely within their formation, while also minimizing fuel usage
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