Rubens H. Korogui

Analysis and Synthesis of Robust Control Systems Using Linear Parameter Dependent Lyapunov Functions

This note provides sufficient robust stability conditions for continuous time polytopic systems. They are obtained from the Frobenius-Perron Theorem applied to the time derivative of a linear parameter dependent Lyapunov function and are expressed in terms of linear matrix inequalities (LMI). They contain as special cases, various sufficient stability conditions available in the literature to date. As a natural generalization, the determination of a guaranteed H2 cost is addressed. A new gain parametrization is introduced in order to make possible the state feedback robust control synthesis using parameter dependent Lyapunov functions through linear matrix inequalities. Numerical examples are included for illustration

H 2 robust filter design with performance certificate via convex programming

In this paper a new approach to H 2 robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of the most expressive methods available for H 2 robust filter design, a new one based on a performance certificate calculation is presented. The performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the H 2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear, rational and causal filters. The calculations are performed through convex programming methods developed to deal with linear matrix inequality (LMI). Many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs.

On a Rational Transfer Function-Based Approach to

This paper introduces a new procedure for H∞ filter design of time-delay linear systems. A finite-order LTI system, called comparison system, is defined in such a way that its H∞ norm is proven to be strongly related to the one of the time-delay system. Differently from what can be viewed as a common feature of filter design methods available in the literature to date, the one presented here treats the filtering design of time-delay systems with classical numerical routines based on Riccati equation and H∞ theory of LTI systems. The proposed algorithm is simple, efficient and easy to implement. Illustrative examples are solved and discussed in order to put in evidence the most relevant properties of the theoretical results. Furthermore, a practical application is presented.

{\cal H}_{\infty}

Robust dynamic output feedback design is an open problem, computationally speaking, since its determination asks for the solution of nonlinear matrix inequalities, namely bilinear ones. This is particularly the case, for polytopic uncertainty. Here a new sufficient condition is proposed by the use of bounds and scaling for completion of squares. The usefulness of the provided conditions stands in the fact that its solution can be performed using the Frank-Wolfe algorithm which runs in only one shot. The control design of an inverted pendulum with uncertain friction coefficients illustrates the theory.

Filtering Design for Time-Delay Linear Systems

Abstract This paper provides robust stability conditions for continuous and discrete time polytopic systems. They are obtained from linear and fractional parameter dependent Lyapunov functions and are expressed in terms of linear matrix inequalities-LMI. As an immediate generalization, a tight upper bound of the associated guaranteed H 2 cost is determined. Numerical examples are included for illustration and comparison purpose with other robust stability conditions for continuous and discrete time systems available in the literature to date.

On Robust Output Feedback Control For Polytopic Systems

This paper considers the problem of H∞ filter design for time-delay systems. An LTI finite dimensional system, called comparison system, is constructed in order to exploit recent results on stability analysis and H∞ norm calculation, which were proven to be strongly related to those of time-delay systems. Differently of what can be viewed as a common feature of filter design methods available in the literature to date, the one presented here addresses time-delay systems filtering with classical numeric routines based on Riccati equation and H∞ theory of LTI systems. The design algorithm is simple, efficient and easy to implement. An illustrative example is solved and is used to put in evidence the most important characteristic of the design procedure.

MATRIX QUADRATIC POLYNOMIALS WITH APPLICATION TO ROBUST STABILITY ANALYSIS

This paper introduces a new approach to H2 robust filtering design for discrete LTI systems subjected to linear fractional parameter uncertainty representation. We calculate a performance certificate in terms of the gap between the lower and the upper bounds of a minimax programming problem, which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load.

On a rational transfer function-based approach to ℋ ∞ filter design for time-delay linear systems

Abstract This paper introduces a new approach to H 2 robust filtering design for continuous-time LTI systems subject to linear fractional parameter uncertainty representation. The novelty consists on the determination of a performance certificate, in terms of the gap between lower and upper bounds of a minimax programming problem which defines the optimal robust equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of a practical application involving an induction motor with uncertain leakage inductance.

Robust H 2 filtering for discrete LTI systems with linear fractional representation

This article introduces a new approach to ℋ2 robust filtering design for continuous and discrete-time LTI systems subjected to linear fractional parameter uncertainty representation. The novelty consists on the determination of a performance certificate in terms of the gap between lower and upper bounds of a minimax programming problem which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load.