César-Fernando Méndez-Barrios

Stability crossing boundaries and fragility characterization of PID controllers for SISO systems with I/O delays

This paper focuses on the closed-loop stability analysis of single-input-single-output (SISO) systems subject to input (or output) delays in the presence of PID-controllers. More precisely, using a geometric approach, we present a simple and user-friendly method for the closed-loop stability analysis as well as for the fragility of such PID controllers. The proposed approach is illustrated on several examples encountered in the control literature.

Output feedback stabilisation of single-input single-output linear systems with I/O network-induced delays. An eigenvalue-based approach

This work addresses the output feedback stabilisation problem for a class of linear single-input single-output systems subject to I/O network delays. More precisely, we are interested in the characterisation of the set of delay and gain parameters guaranteeing the stability of the closed-loop system. To perform such an analysis, we adopt an eigenvalue perturbation based approach. Various illustrative numerical examples complete the presentation.

Proportional-delayed controllers design for LTI-systems: a geometric approach

ABSTRACT This paper focuses on the design of P-δ controllers for single-input-single-output linear time-invariant systems. The basis of this work is a geometric approach allowing to partitioning the parameter space in regions with constant number of unstable roots. This methodology defines the hyper-planes separating the aforementioned regions and characterises the way in which the number of unstable roots changes when crossing such a hyper-plane. The main contribution of the paper is that it provides an explicit tool to find P-δ gains ensuring the stability of the closed-loop system. In addition, the proposed methodology allows to design a non-fragile controller with a desired exponential decay rate σ. Several numerical examples illustrate the results and a haptic experimental set-up shows the effectiveness of P-δ controllers.

Closed-loop stability analysis of voltage mode buck using a proportional-delayed controller

This paper focuses on the design of a Ρ-δ controller for the stabilization of a buck DC/DC converter. The basis of this work is a geometric approach which allows to partition the parameters space into regions with constant number of unstable roots. The main contribution of the paper is that it provides an explicit tool to find Ρ-δ gains ensuring the stability of the closed-loop system. In addition, the proposed methodology enables the design a non-fragile controller with a desired exponential decay rate σ. In order to illustrate the effectiveness of the proposed controller, some numerical examples are presented.

Stability and instability intervals of polynomially dependent systems: An matrix pencil analysis

In this paper we present a stability analysis approach for polynomially-dependent one-parameter systems. The approach, which appears to be conceptually appealing and computationally efficient and is referred to as an eigenvalue perturbation approach, seeks to characterize the analytical and asymptotic properties of eigenvalues of matrix-valued functions or operators. The essential problem dwells on the asymptotic behavior of the critical eigenvalues on the imaginary axis, that is, on how the imaginary eigenvalues may vary with respect to the varying parameter. This behavior determines whether the imaginary eigenvalues cross from one half plane into another, and hence plays a critical role in determining the stability of such systems. Our results reveal that the eigenvalue asymptotic behavior can be characterized by solving a simple generalized eigenvalue problem, leading to numerically efficient stability conditions.

Stability Analysis of Polynomially Dependent Systems by Eigenvalue Perturbation

In this technical note we present a stability analysis approach for polynomially-dependent one-parameter systems. The approach, which appears to be conceptually appealing and computationally efficient and is referred to as an eigenvalue perturbation approach, seeks to characterize the analytical and asymptotic properties of eigenvalues of matrix-valued functions or operators. The essential problem dwells on the asymptotic behavior of the critical eigenvalues on the imaginary axis, that is, on how the imaginary eigenvalues may vary with respect to the varying parameter. This behavior determines whether the imaginary eigenvalues cross from one half plane into another, and hence plays a critical role in determining the stability of such systems. Our results reveal that the eigenvalue asymptotic behavior can be characterized by solving a simple generalized eigenvalue problem, leading to numerically efficient stability conditions.

Sampling decomposition and asymptotic zeros behaviour of sampled-data SISO systems. An eigenvalue-based approach

This paper deals with some problems concerning the zero behaviour of a class of sampled-data SISO systems. More precisely, given a continuous-time system, we derive all the sampling intervals guaranteeing the invariance of the number of unstable zeros in each interval. To perform such an analysis, we adopt an eigenvalue perturbation-based approach. Various illustrative numerical examples complete the presentation.