Domingos C. W. Ramos

An LMI condition for the robust stability of uncertain continuous-time linear systems

A new sufficient condition for the robust stability of continuous-time uncertain linear systems with convex bounded uncertainties is proposed in this note. The results are based on linear matrix inequalities (LMIs) formulated at the vertices of the uncertainty polytope, which provide a parameter dependent Lyapunov function that assures the stability of any matrix inside the uncertainty domain. With the aid of numerical procedures based on unidimensional search and the LMIs feasibility tests, a simple and constructive way to compute robust stability domains can be established.

A less conservative LMI condition for the robust stability of discrete-time uncertain systems

Abstract In this paper, a less conservative condition for the robust stability of uncertain discrete-time linear systems is proposed. The uncertain parameters, assumed to be time-invariant, are supposed to belong to convex bounded domains (polytope type uncertainty). The stability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope domain. A simple and numerically efficient feasibility test provides a set of Lyapunov matrices whose convex combination can be used to assess the stability of any dynamic matrix inside the uncertainty domain. Examples illustrate the results.

An LMI approach to compute robust stability domains for uncertain linear systems

A simple and constructive way to establish maximum robust stability domains for continuous-time uncertain linear systems with convex bounded uncertainties is proposed in,this paper. The results are based on sufficient conditions formulated in terms of linear matrix inequalities, which provide a parameter dependent Lyapunov function that assures the stability of any matrix inside the uncertainty domain. The numerical procedures are entirely based on unidimensional search and linear matrix inequalities feasibility tests.

Estabilidade robusta de sistemas lineares através de desigualdades matriciais lineares

Sufficient conditions for the analysis of stability of linear systems with polytopic uncertainties are presented in this paper. The robust stability is guaranteed by the existence of a parameter dependent Lypaunov function obtained from the feasibility test of a set of linear matrix inequalities (LMIs) formulated at the vertices of the uncertainty polytope. Three conditions are presented, and the results are also compared with the analysis based on quadratic stability (same Lyapunov function for the entire set of uncertainties), for continuous as well as discrete-time systems. The first condition exploits the use of some extra variables (matrices) in the LMIs, and the second one uses a larger number of LMIs. These two conditions have recently appeared in the literature and are less conservative than quadratic stability. The third condition, proposed in this paper, combines the two ideas, yielding better results, and contains the previous conditions as particular cases. Several examples are presented to illustrate the numerical performance of the LMI conditions in terms of efficiency and computational complexity.

ROBUST CONTROL SYNTHESIS VIA A GENETIC ALGORITHM AND LMIS

Abstract This paper is concerned with the use of genetic algorithms for robust control synthesis, in a context where there is no convex formulation for such design. For that aim, a robustness analysis condition is given in terms of a linear matrix inequality feasibility problem, producing less conservative results than recent parameter dependent Lyapunov based methods (which encompasses quadratic stability) for polytopic uncertainties in linear systems. Since the design criterion is a closed-loop test formulated in the controller parameter space, any control structure constraint is allowed, such as: low-order dynamic controllers, static output feedback controllers, decentralized control, etc. The role of genetic algorithms for the design of “less conservative” and “structure-constrained” controllers is discussed.

Alternative LMIs characterization of H 2 and central H ∞ discrete-time controllers

This paper proposes alternative LMIs characterization for the /spl Hscr//sub 2/ and the central /spl Hscr//sub /spl infin// state feedback controllers for discrete-time systems, allowing the immediate extension to handle uncertain systems belonging to convex polyhedral domains.

Alternative LMIs characterization of /spl Hscr//sub 2/ and central /spl Hscr//sub /spl infin// discrete-time controllers

This paper proposes alternative LMIs characterization for the /spl Hscr//sub 2/ and the central /spl Hscr//sub /spl infin// state feedback controllers for discrete-time systems, allowing the immediate extension to handle uncertain systems belonging to convex polyhedral domains.

Alternative LMIs characterization of ℋ/sub 2/ and central ℋ/sub ∞/ discrete-time controllers

This paper proposes alternative LMIs characterization for the /spl Hscr//sub 2/ and the central /spl Hscr//sub /spl infin// state feedback controllers for discrete-time systems, allowing the immediate extension to handle uncertain systems belonging to convex polyhedral domains.