Cristiano M. Agulhari

LMI Relaxations for Reduced-Order Robust

This technical note is concerned with the problem of reduced order robust H∞ dynamic output feedback control design for uncertain continuous-time linear systems. The uncertain time-invariant parameters belong to a polytopic domain and affect all the system matrices. The search for a reduced-order controller is converted in a problem of static output feedback control design for an augmented system. To solve the problem, a two-stage linear matrix inequality (LMI) procedure is proposed. At the first step, a stabilizing state feedback scheduled controller with polynomial or rational dependence on the parameters is determined. This parameter-dependent state feedback controller is used at the second stage, which synthesizes the robust (parameter-independent) output feedback H∞ dynamic controller. A homogeneous polynomially parameter-dependent Lyapunov function of arbitrary degree is used to assess closed-loop stability with a prescribed H∞ attenuation level. As illustrated by numerical examples, the proposed method provides better results than other LMI based conditions from the literature.

{\cal H}_{\infty}

This paper is concerned with the problem of robust static output feedback control design for continuous-time uncertain linear systems. The uncertain time-invariant parameters belong to a polytopic domain and affect all system matrices. A two-stage linear matrix inequality procedure is proposed. At the first step, a stabilizing state feedback scheduled gain with polynomial or rational dependence on the parameters is determined. This state feedback gain is used as an input parameter for the second stage, which synthesizes the robust static output feedback gain. In both stages, a homogeneous polynomially parameter-dependent Lyapunov function of arbitrary degree is used to assess closed-loop stability. Numerical examples demonstrate that with the increase of the degree of the polynomial matrices more accurate results are obtained, outperforming the existing methods in the literature.

Control of Continuous-Time Uncertain Linear Systems

This paper investigates the problem of designing ℋ∞ robust output-feedback controllers for uncertain discrete-time linear systems with time-invariant parameters lying in polytopic domains. The computation procedure is based on linear matrix inequalities and is performed in two steps. The first stage designs a parameter-dependent state-feedback controller, that is used as an input parameter for the second stage, which synthesizes the desired robust ℋ∞ output-feedback gain. The conditions are based on parameter-dependent Lyapunov functions and can deal with uncertainties in the output matrix of the system. Numerical examples illustrate the advantages of the proposed method when compared to other techniques available in the literature.

Static output feedback control of polytopic systems using polynomial Lyapunov functions

A compression method, based on the choice of a wavelet that minimizes the distortion of compression for each electrocardiogram considered, is proposed in this paper. The scaling filter used on the determination of the wavelet function is obtained from the resolution of an optimization problem, which is unconstrained since the scaling filter is parametrized in a way that the constraints applied to the scaling filter are embedded on the parameters. The coefficients of projection of the signal over the wavelet subspaces are calculated and only the most significant ones are retained, being the significant coefficients determined in order to satisfy a pre-specified distortion measure. The bitmap that informs the positions of the retained coefficients is encoded along with the values of the coefficients by using an improved version of the Run Length Encoding technique. Experiments that compare the proposed approach with other techniques illustrate the efficiency of the method.

Robust ℋ ∞ static output-feedback design for time-invariant discrete-time polytopic systems from parameter-dependent state-feedback gains

This paper proposes a design procedure for reduced-order dynamic output feedback (DOF) gain-scheduling controllers with H∞ guaranteed cost for linear parameter-varying (LPV) continuous-time systems, where the measurement of the scheduling parameters may be affected by uncertainties. Thanks to the flexibility of the proposed modeling, the LPV-DOF controllers can be implemented in terms of a selected set of parameters, which are supposed to be available for measurement in real time. The design conditions can cope with both additive and multiplicative noises, considered as time-varying uncertainties, affecting the measures. All parameters and uncertainties are modeled through the multi-simplex framework, i.e., the Cartesian product of simplexes. The problem is solved through a two-stage procedure based on linear matrix inequalities.

An Adaptive Run Length Encoding method for the compression of electrocardiograms

A compression method, based on the choice of a wavelet that matches the electrocardiogram signal to be compressed, is proposed in this paper. The coefficients of the scaling filter that minimize the distortion of the compressed signal are used to determine the wavelet. The choice of the scaling filter is done by the parametrization of the scaling coefficients in a way that all the constraints are satisfied for any set of parameters. A genetic algorithm is used to determine the parameters that minimize the distortion of the compressed signal. The performance of the proposed algorithm is analyzed and compared with the compression using the classical wavelet Db3.

ℋ ∞ dynamic output feedback for LPV systems subject to inexactly measured scheduling parameters

A compression method, based on the choice of a wavelet that matches the electrocardiogram signal to be compressed, is proposed in this paper. The scaling filter that minimizes the distortion of the compressed signal are used to determine the wavelet. The scaling filter is used to generate the coefficients of projection of the ECG signal in the scaling and wavelet subspaces, and only the most significant coefficients are retained. Coding methods are applied to the retained coefficients in order to improve the compression.

A genetic algorithm to compress electrocardiograms using parameterized wavelets

This paper is devoted to the problem of computing control laws for the stabilization of continuous‐time linear time‐varying systems. First, a necessary and sufficient condition to assess the stability of a linear time‐varying system based on the norm of the transition matrix computed over a sequence of successive finite‐time intervals is proposed. A link with a stability condition for an equivalent discrete‐time model is also established. Then, 3 approaches for the computation of stabilizing state‐feedback gains are proposed: a continuous‐time technique, ie, directly derived from the stability condition, not suitable for numerical implementation; a method based on the stabilization of the discrete‐time equivalent model along with a transformation to generate the desired continuous‐time gain; and the computation of stabilizing gains for a set of periodic discrete‐time systems. Finally, by adapting one of the existing methods for the stabilization of periodic discrete‐time systems, an algorithm for the computation of a stabilizing state‐feedback continuous‐time gain is proposed. A numerical example illustrates the validity of the technique.

Compressing electrocardiogram signals using parameterized wavelets

New conditions for the design of robust periodic observer-based controllers for periodic discrete-time linear time-varying (LTV) systems are proposed in this paper. The control system is designed to be robust to external noises, and such robustness is achieved by minimizing the ℋ∞ norm from the input noise to the error output in the observer design, and the ℋ∞ norm from the error and disturbance signal to the output in the control design. Concerning the observer, two LMI (Linear Matrix Inequality) conditions are proposed. As part of the main contribution, an LMI condition, based on a dual representation of the LTV system, is also proposed for the synthesis of a robust state-feedback controller that makes use of the observed states rather than the actual states. A numerical example illustrates the validity of the proposed technique.

A new methodology to compute stabilizing control laws for continuous-time LTV systems: A new methodology to compute control laws for LTV systems

Abstract A procedure to synthesize stabilizing controllers for linear time-varying periodic continuous-time systems is proposed in this paper. The controller is a periodic state-feedback gain whose construction is based on the utilization of the transition matrix of the open-loop system, and the stability of the closed-loop system is guaranteed if the system is controllable and if a observability-based condition is satisfied. The periodic state feedback gain is obtained through the numerical integration of two differential matrix equations over two periods, being the resolution of such equations considerably simpler and computationally more viable than the resolution of Ricatti differential equations considered in the standard LQR approach. Some examples illustrates the validity of the technique.