Robust state feedback synthesis for control of non-square multivariable nonlinear systems Srinivas Palanki a, *, Juan C. Cockburn b , Soumitri N. Kolavennu c a Department of Chemical Engineering, Florida A&M University-Florida State University, Tallahassee, FL 32310-6046, USA b Department of Electrical Engineering, Florida A&M University-Florida State University, Tallahassee, FL 32310-6046, USA c Honeywell Laboratories, 3660 Technology Drive, Minneapolis, MN 55418, USA Abstract In this paper, a robust nonlinear controller is designed in the Input/Output (I/O) linearization framework, for non-square multivariable nonlinear systems that have more inputs than outputs and are subject to parametric uncertainty. A nonlinear state feedback is synthesized that approximately linearizes the system in an I/O sense by solving a convex optimization problem online. A robust controller is designed for the linear uncertain subsystem using a multi-model H 2 =H 1 synthesis approach to ensure robust stability and performance of non-square multivariable, nonlinear systems. This methodology is illustrated via simulation of a reg- ulation problem in a continuous stirred tank reactor. # 2002 Elsevier Ltd. All rights reserved. Keywords: Non-square Multivariable systems, Robust control, I/O linearization 1. Introduction In the last two decades, there has been a significant effort in the development of the Input/Output (I/O) lin- earization approach to design controllers for multi- variable nonlinear systems [1]. The general design approach for this class of methods has been to develop a state feedback which makes the closed-loop system lin- ear in an input–output sense as well as decoupled (i.e., one inputs affects only one output). Then, a linear con- troller is designed for this linear system for desired per- formance. However, the state feedback design requires an exact description of the process, which is generally not available. Due to modeling uncertainty, input–out- put linearity as well as decoupling may be lost. This can result in severe degradation in controller performance as well as loss of stability. Motivated by this limitation, there has been active research in the past decade in the area of approximate linearization via feedback. There are different approaches to approximate linearization depending on the description of the uncertainty and the particular application under consideration. A review of various approximate linearization approaches can be found in [2]. In this paper, we consider the development of a robust controller in the I/O setting for a system with parametric uncertainty. The system is approxi- mately linearized based on nominal parameter values of the system. Then a robust outer-loop controller is designed for the ‘‘approximately linearized’’ system. In the past decade, several tools have been developed in linear robust control theory [3,4]. The issue of robust controller design in the Input/Output (I/O) linearization framework for nonlinear systems has attracted attention recently. However results are available primarily for SISO systems (see [5–7] square MIMO systems (see [8–10]); the controller design issues for non-square multivariable systems (systems where the number of inputs is not equal to the number of outputs) in the face of para- metric uncertainty are not well understood. In this paper, we extend the multi-model approach of Kolavennu et al. [10] to non-square systems. In the multi-model H 2 =H 1 approach, the plant is described by a set of linear time invariant models and a controller is designed which achieves good quadratic performance while at the same time satisfies specified robustness cri- teria. This approach has been demonstrated successfully for chemical process control problems represented by linear systems [11] and square I/O linearizable nonlinear systems [10]. Non-square systems occur frequently in the chemical process industry. However, for controller 0959-1524/03/$ - see front matter # 2002 Elsevier Ltd. All rights reserved. PII: S0959-1524(02)00098-7 Journal of Process Control 13 (2003) 623–631 www.elsevier.com/locate/jprocont * Corresponding author. Tel.: +1-850-410-6163; fax: +1-850-410- 6150. E-mail address: palanki@eng.fsu.edu (S. Palanki).