ROBUST POLE ASSIGNMENT BY STATE FEEDBACK CONTROL USING INTERVAL ANALYSIS Marcia L. M. Prado, Alfredo D. S. Lordelo, Paulo A. V. Ferreira University of Campinas School of Electrical and Computer Engineering Campinas, SP 13083-852 Brazil E-mail: valente@dt.fee.unicamp.br Abstract: An interval analysis approach for the design of robust state feedback controllers is proposed. It is shown that when regional pole placement specifications are represented as spectral sets of interval polynomials, the robust state feedback design problem can be entirely formulated and solved in the context of the concepts and methods of interval analysis. Explicit convex polyhedral representations of a class of robust state feedback controllers satisfying an interval Ackerman’s equation are derived. A design procedure based on nonlinear programming which aims at maximizing the non-fragility of the resulting robust controller is introduced. Numerical examples illustrate the design of robust state feedback controllers through the interval analysis approach proposed. Copyright c 2005 IFAC Keywords: Uncertain linear systems, pole assignment, intervals, polynomials, numerical algorithms. 1. INTRODUCTION The problem of designing state feedback con- trollers for linear time-invariant systems has been extensively treated in the control system litera- ture. Stabilizability conditions via constant state feedback, as well as state feedback solutions for pole placement problems under the assumption of a precisely known system have been completely characterized (Chen, 1999). However, linear mod- els of real systems sometimes include parameters whose values are unknown but bounded in com- pact sets, often described in the form of closed in- tervals. In this case, stabilization and performance via state feedback must be addressed in a robust sense. The robust control problem consists in find- 1 This work has been partially supported by grants from CAPES and CNPq, Brazil. ing a state feedback gain so as to place all closed- loop poles in the left-half side of the complex plane (robust stabilization) or in some prescribed region of it (robust performance) for every possible set of system parameters. The robust stabilization problem has been tackled through two distinct approaches (Wei, 1994). In the first one, the uncer- tain system is viewed as a nominal system subject to perturbations. The problem is decomposed into subproblems of stabilizing the nominal system and then proving that the closed-loop system remains stable in spite of all the admissible perturbations. According to the second approach, the stabiliz- ability of the system is initially determined and then a stabilizing control is designed. In this paper a robust state feedback approach for linear time-invariant interval systems which combines some of the above characteristics is