Linear Systems In Presence Research Articles

Observer Synthesis for Uncertain Linear Systems under Multiple Sampled Outputs: Application to a Building-Like Structure

In this work a full-state observer is presented for MIMO linear systems in presence of uncertainties and multiple sampled outputs. The observer is capable to reconstruct the state vector in a continuous form even if it recieves the output in a sampled form. Then, it is possible to establish that the observation error will converge to a bounded value depending on the magnitude of the maximum sampling interval and uncertainties. In the case when there is no uncertainties, the observation error converges to zero. The proposed observer is tested to estimate the state vector in a building structure in which the seismic signal is treated as uncertainty.

Integral sliding mode H$$_\infty $$ control of fractional system in presence of unmatched disturbance

In this paper, $${H}_{\infty }$$ control for fractional order linear system in presence of unmatched disturbance is considered. Fractional order disturbance observer is designed to evaluate the unmatched disturbance. With choosing proper observer gain, the bounded convergence of the evaluated error is obtained. Afterwards an integral sliding mode surface is given on the basis of the disturbance estimation. Using linear matrix inequality technology, the state feedback controller is provided, which ensure the closed-loop system satisfy $${H}_{\infty }$$ performance. Finally, numerical example is given to illustrate the robustness of the designed control strategy.

Robust $$\mathcal{H}_\infty$$ Observer-based Stabilization of Linear Discrete-time Systems with Parameter Uncertainties

This paper addresses the problem of observer-based stabilization of discrete-time linear systems in presence of parameter uncertainties and l2-bounded disturbances. We propose a new variant of the classical two-step LMI approach. In the first step, we use a slack variable technique to solve the optimization problem resulting from stabilization by a static state feedback. In the second step, a part of the slack variable obtained is incorporated in the $$\mathcal{H}_\infty$$ observer-based stabilization problem, to calculate simultaneously the Lyapunov matrix and the observer-based controller gains. The effectiveness of the proposed design methodology is demonstrated using the dynamic model of a quadruple-tank flow process system. Additional numerical illustrations are presented to show the superiority of the proposed Modified Two-Step Method (MTSM) from a LMI feasibility point of view.

Identification scheme for switched linear systems in presence of bounded noise

This paper proposes an online switched linear system identification algorithm based on a modified outer bounding ellipsoid algorithm. It alternates between estimating discrete states and system parameters. This algorithm can be adapted to solve offline identification as well as MIMO system identification. Some geometric intuition is also provided. Simulation results show that the algorithm has improvement in both estimation error and computation time over existing algorithms.

Identification scheme for switched linear systems in presence of bounded noise

This paper proposes an online switched linear system identification algorithm based on a modified outer bounding ellipsoid algorithm. It alternates between estimating discrete states and system parameters. This algorithm can be adapted to solve offline identification as well as MIMO system identification. Some geometric intuition is also provided. Simulation results show that the algorithm has improvement in both estimation error and computation time over existing algorithms.

Tracking Controller Design for Linear Systems in Presence of Multiple Saturation Constraints

We are considering the problem of controlling discrete-time linear systems that are subject to multiple saturation constraints. Specifically, we consider systems that are driven by an actuator whose output is subject to magnitude plus rate saturations. Moreover, the output of the considered plant is supposed to be intrinsically saturating. Then, aiming to guarantee the tracking of (compatible) reference signals, a suitable saturated linear controller is designed and the closed loop of the control system is analyzed using input–output stability approach. This allows defining the necessary conditions that ensure good tracking performances. Namely, it is shown that perfect output-reference tracking could be ensured in case of varying with $$l_{2}$$ -vanishing rate inputs. In addition, in case of arbitrary reference inputs, it is shown that the less changing (in the mean) the inputs are, the better the average (output-reference) tracking quality is. This result entails good matching features as the system dynamics are assumed to be non-minimum phase and subject to multiple saturation constraints. A numerical example is provided to illustrate the application of the proposed control strategy.

Sliding mode control for uncertain input delay fractional order systems

A sliding mode control is developed for robust stabilization of fractional-order input-delay linear systems in presence of uncertainties and external disturbances. First, a fractional-order state predictor is used to compensate the delay in the input control. Second, a robust sliding mode control is proposed in order to stabilize the system and to thwart the effect of model uncertainties and external disturbances. The sliding mode controller is designed by considering a sliding surface defined by fractional order integral. Conditions for the existence and finite time reaching of the sliding mode in presence on bounded uncertainties and bounded external disturbances are established. Further, the stability of the closed loop system on the sliding mode is analyzed by using recent results on Lyapunov stability theory for fractional order systems. A numerical example is given to illustrate some theoretical results.

Sufficient Conditions for Robust Input-Output Finite-Time Stability of Linear Systems in Presence of Uncertainties

AbstractThe concept of Bounded-Input Bounded-Output (BIBO) stability arises when one wants to focus on the study of the the input-output behavior of a dynamical system, as opposed to the classical Lyapunov stability. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input-Output FTS. A system is said to be IO finite time stable if, assigned a bounded input class and some boundaries in the output signal space, the output never exceeds such boundaries over a prespecified (finite) interval of time. IO-FTS has been already investigated in previous papers, whereas this is the first work dealing with the input-output behavior of an uncertain dynamical system in the FTS framework. Two sufficient conditions are given, concerning the class of 2 and ∞ input signals, for the analysis of robust IO-FTS. The applicability of the results is illustrated by means of a numerical examples.

BIBO stabilization of piecewise switched linear systems with delays and nonlinear perturbations

This paper deals with BIBO stabilization of piecewise switched linear systems in presence of delays and nonlinear perturbations. Based on piecewise quadratic Lyapunov functional, the main contribution of the paper is the derivation of sufficient conditions of BIBO stabilization in the form of algebraic Riccati matrix equation. The robust quadratic stability for such system is also discussed. A numerical example is given to illustrate the effectiveness of the theoretical results.

Robust Reduced-order Output-feedback H∞ Control

The problem of robust H∞ reduced-order control design for linear systems in presence of polytopic type uncertainties is addressed. The controller is obtained by transforming the problem into a robust static output-feedback control design problem. Applying a recent method for solving the latter by means of linear matrix inequalities, a sufficient condition is obtained for the existence of a solution to the problem. A simple method for deriving the reduced-order controller is given in the case where the latter condition is satisfied.

Linear control of nonlinear systems based on nonlinearity measures

In reality, virtually every process is a nonlinear system. Nevertheless, linear controller design methods have proved to be adequate in many applications. In practice, the linear controller design is usually done disregarding a possible nonlinear plant/linear model mismatch. In this work we introduce a general framework for the development of linear controllers for nonlinear systems based on nonlinearity measures. Nonlinearity measures are tools to assess the extent of a system’s inherent nonlinearity instead of just recognizing a system as being linear or nonlinear. Recent work shows that nonlinearity measures characterize the magnitude of the modeling error when an optimal linear model is used for the nonlinear system. The best linear model can then be used to design a linear controller that robustly stabilizes the linear system in presence of the nonlinear modeling error. A crucial point is that both, the best linear model and the modeling error, are determined for a specified region of operation, thus significantly increasing the class of applicable nonlinear systems. Examples demonstrate the (necessity and) effectiveness of the proposed approach.

A SWITCHING SCHEME FOR THE ROBUST STABILIZATION OF DISCRETE TIME SYSTEMS WITH UNMATCHED UNCERTAINTIES

In this paper robust control of discrete time linear systems in presence of unmatched uncertainties is considered. Discrete time Variable Structure Control is used, and the presence of the sector, always affecting this control approach, is avoided by means of Switching Control. This latter is based on a suitable partition of the parameter space, while each single controller is based on Discrete time Variable Structure Control. It is worth noticing that the proposed approach does not depend on the duration of the sampling interval, hence it works both for sampled data system and for “pure” discrete time systems.

ROBUST STABILITY ANALYSIS OF LINEAR SYSTEMS WITH TIME-VARYING DELAYS

Robust stability of linear systems in presence of bounded uncertain time-varying time delays is studied. The time delay robustness problem is treated in the Integral Quadratic Constraint (IQC) framework. The stability criterion is formulated as frequency dependent linear matrix inequalities. The criterion can be equivalently formulated as a Semi-Definite Program (SDP) by applying Kalman-Yakubovich-Popov (KYP) lemma. Therefore, checking the criterion can be done efficiently by using various SDP solvers.

Semiglobal regulation of linear systems in presence of measurement constraint

In this note, we consider the problem of output regulation for linear single-input-single-output systems in presence of time-varying measurement constraint. It is shown how an internal model-based regulator, processing a saturated uncertain function of the regulated error, can be designed in order to secure asymptotic tracking/rejection of exosystem-generated references/disturbances. The design is semiglobal in the initial state of the plant and of the exosystem and requires the zero dynamics of the controlled system to be weakly minimum-phase.

A Recursive and Robust Identification Method for a Class of Nonlinear Systems

Abstract This paper presents a recursive and robust identification method for a class of non linear systems in presence of unknown but bounded errors. Based on the formulation of the input output difference equation of Multi-Input Single-Output (MISO) Wiener Hammerstein model, a modified Weighted Extended-Recursive Least Squares (WE-RLS) procedure is employed to estimate separately parameters of the linear sub-systems and the static non linear elements related to each input when the disturbances upper bound is supposed to be known. The proposed algorithm is performed by minimizing a cost function where a time varying factor is introduced such as the estimated parameters are consistent with the measurements and the noise constraints and, to improve convergence properties. Sufficient conditions to ensure asymptotic convergence are established. Efficiency of the proposed algorithm is shown through a numerical example of high nonlinearities.

Identification of stochastic linear systems in presence of input noise

Most identification methods rely on the assumption that the input is known exactly. However, when collecting data under an identification experiment it may not be possible to avoid noise when measuring the input signal. In the paper some different ways to identify systems from noisy data are discussed. Sufficient conditions for identifiability are given. Also accuracy properties and the computational requirements are discussed. A promising approach is to treat the measured input and output signals as outputs of a multivariable stochastic system. If a prediction error method is applied using this approach the system will be identifiable under mild conditions.