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The so-called nonlinear H∞-control problem in state space is considered with an emphasis on developing machinery with promising computational properties. Both state feedback and output feedback H∞-control problems for a class of nonlinear systems are characterized in terms of continuous positive definite solutions of algebraic nonlinear matrix inequalities which are convex feasibility problems. The issue of existence of solutions to these nonlinear matrix inequalities (NLMIs) is justified.

Primal-dual interior-point methods have proven to be very successful for both linear programming (LP) and, more recently, for semidefinite programming (SDP) problems. Many of the techniques that have been so successful for LP have been extended to SDP. In fact, interior point methods are currently the only successful techniques for SDP. Research supported by Natural Sciences Engineering Research Council Canada. Email sgkruk@acm.org y Department of Mechanical Engineering, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102 Japan z Technische Universitat Graz, Institut fur Mathematik, Steyrergasse 30, A-8010 Graz, Austria x EMS Program Director, ACE-42 E-Quad, Princeton University, Princeton NJ 08544, Tel: 609-2580876, Fax: 609-258-3796, E-mail rvdb@princeton.edu, http://www.princeton.edu/~rvdb/ -- Research supported by Natural Sciences Engineering Research Council Canada. Email hwolkowi@orion.math.uwaterloo.ca, http://orion.math.uwaterloo.ca/~hwolkowi 0 This report is av...

In this paper, the problem of determining the worst-case H 2 performance of a control system subject to linear time-invariant uncertainties is considered. A set of upper bounds on the performance is derived, based on the theory of stability multipliers and the solution of an original optimal control problem. The numerical issues raised by the resulting computational problems are discussed: in particular, newly developed interiorpoint convex optimization methods, combined with Linear Matrix Inequalities apply very well to the fast and accurate solution of these problems. The new results compare favorably with prior ones. The method can be extended to other types of perturbations.

robustness, linear matrix inequalities. A wheel slip controller for Anti-lock Brake Systems (ABS) is designed using LQ-optimal control. The controller gain matrices are gain scheduled on the vehicle speed. A parameter dependent Lyapunov function for the nominal linear parameter varying (LPV) closed loop system is found by solving a linear matrix inequality (LMI) problem. This Lyapunov function is used to investigate robustness with respect to uncertainty in the road/tyre friction characteristic. Experimental results from a test vehicle with electromechanical brake actuators and brake-by-wire show that high performance and robustness are achieved. 1

Recent papers have demonstrated the e ectiveness of our iterative algorithm using linear matrix inequalities (LMI's) on several parametric robust H1 control designs. This paper presents two additional important components to the discussion on the behavior of the new LMI-based iterative algorithm: a comparison study between the LMI synthesis technique and the existing iterative approaches of the complex and mixed =Km synthesis, and a convergence analysis of this new algorithm. The results indicate that the Popov H1 controller synthesis provides a viable alternative for designing real parametric robust controllers and exhibits properties similar to the D{K and D,G{K iteration of the complex and mixed =Km synthesis. The key potential advantage of using the LMI approach is the elimination of the curve- tting for the D and G scaling functions. 1

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