Antonio Barreiro

Brief paper: Analysis of networked control systems with drops and variable delays

Motivated by the insertion of a communication network in the feedback control loop, this paper focuses on how network-induced data dropouts and variable delays affect the stability of a linear plant with state feedback control. Sufficient conditions for Lyapunov stability are derived in the case of uncertainty due to drops and delays. The verification problem of the sufficient conditions can be directly cast as an LMI feasibility problem. We illustrate the methodology by an example in the cases of drops, delays and drops with delays.

Delay-Independent Stability of Reset Systems

Reset control systems have potential advantages to overcome fundamental limitations of LTI compensation. However, since a reset compensator may destabilize a stable base LTI system, stability needs to be guaranteed in advance for a proper practical application of reset control. This works extends previous stability results of reset control systems to consider the case of LTI plants with time-delays. Stability independent of the delay criteria are developed both by means of LMIs and in the frequency domain by using the KYP Lemma.

Brief paper: Delay-dependent stability of reset systems

This work presents results on the stability of time-delay systems under reset control. The case of delay-dependent stability is addressed, by developing a generalization of previous stability results for reset systems without delay, and also a generalization of the delay-independent case. The stability results are derived by using appropriate Lyapunov-Krasovskii functionals, obtaining LMI (Linear Matrix Inequality) conditions and showing connections with passivity and positive realness. The stability conditions guarantee that the reset action does not destabilize the base LTI (Linear Time Invariant) system. Several interpretations are given for these conditions in terms of impulsive control, which provide insights into the potentials of reset control.

Reset Times-Dependent Stability of Reset Control Systems

Reset control systems are a special type of hybrid systems in which the time evolution depends both on continuous dynamics between resets and the discrete dynamics corresponding to the reset instants. In this work, stability of reset control systems is approached by using an equivalent (time-varying) discrete time system, introducing necessary and sufficient stability conditions that explicitly depends on the reset times. These conditions have been simplified for the case in which the linear base control system is stable, resulting in a sufficient condition that only depends on a lower bound of the reset intervals.

Generic Approach to Stability Under Time-Varying Delay in Teleoperation: Application to the Position-Error Control of a Gantry Crane

In this paper, we develop a generic approach for modeling a teleoperation setup, as a negative single feedback loop containing a linear time-invariant block and an uncertain time-varying delay. It is not based on specific dynamics of masters and slaves, neither on any control architecture. The main added value of the proposed approach is the possibility of deriving frequency-domain conditions for robust stability in the presence of time-varying delays and parametric uncertainties. To address stability, we choose a primitive result providing a bound of certain delay subsystem. We combine this, with input-output stability criteria and μ-analysis and synthesis techniques, to reach a procedure based on the structured singular value providing less conservative results. Finally, our approach is presented within a suggested flowchart that helps the designer to manage the control parameter ranges and facilitates the gradual achievement of stability, robust stability, and performance properties. As a case study, we consider the Internet-based teleoperation of a gantry crane by means of the position-error control architecture. We have also obtained actual delay bounds appearing with UDP protocol for different Internet locations. Simulation and experimental results confirm the robust performance of the teleoperation system in terms of stability and tracking behavior.

Delay-Independent Stability of Reset Control Systems

Reset control systems have potential advantages to overcome fundamental limitations of LTI compensation. However, since a reset compensator may destabilize a stable base LTI system, stability needs to be guaranteed in advance for a proper practical application of reset control. This works extends previous stability results of reset control systems to consider the case of LTI plants with time-delays. Stability independent of the delay criteria are developed both by means of LMIs and in the frequency domain by using the KYP Lemma

Stability of non-linear QFT designs based on robust absolute stability criteria

The paper is mainly devoted to the robust stability problem of non-linear QFT designs. The problem is first formulated for SISO non-linear systems, limited in practice to linear-memoryless sector-bounded non-linear interconnections, and in an I/O stability sense. The work investigates several possible robust adaptations of the Circle Criterion, depending on the type of resulting interconnection of linear and non-linear blocks, appearing in the feedback system. Also, the use of the Popov Criterion is investigated as an alternative less conservative than the Circle Criterion in some cases. The proposed techniques are given in usual QFT language, expressed as frequency conditions or boundaries in the Nichols Chart, allowing an easy integration with other design objectives. In addition, multivariable extensions using a conicity condition and the concept of maximal cone are adopted to give stability boundaries in interconnections of SIMO linear-MISO sector-bounded memoryless blocks. All the robust stability criteria are illustrated using significant examples to emphasize the practical application of the resulting techniques.

Structural identifiability of dynamic systems biology models

A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areas.

Brief Robust stability of fuzzy control systems based on conicity conditions

This paper deals with the robust stability problem for a feedback system with a fuzzy controller. The problem is treated using the small-gain and conicity criteria for nonlinear stability. Robustness is addressed in terms of multiplicative perturbations and stability margins. Compensator design is based on an initial set of rules (the previous design), reflecting an approximate formulation of the desired performance. The previous design is refined and modified to achieve a prescribed robustness margin. We impose in the design procedure that the required changes have to be as small as possible. In this way, the final solution is the better compromise between performance and robust stability. The redesign is based on inequalities on the fuzzy parameters (output centroids) that are derived from small-gain stability conditions. An application example is presented, for a simulated exponential frictional model of a DC servo motor.

Reset control systems with reset band: Well-posedness, limit cycles and stability analysis

Abstract Reset controllers provide a simple way to improve performance when controlling strongly traded-off plants. A reset controller operates most of the time as a linear system, but when some condition holds, it performs a zero resetting action on its state. Recently, some generalizations have been proposed, for example, the anticipation of the reset condition with the so-called reset band . There is a lack of analysis tools for reset systems with reset band. In this paper we address this problem by means of Poincare maps (PM). It is shown how PM can predict the existence and stability of limit cycles, and give also information on pathologies such as Zenoness, and provide parameter ranges where the system is guarded against those behaviors and thus global asymptotical stability (GAS) is guaranteed.