LMIs in Control/Click here to continue/Applications of Non-Linear Systems/Control of Rational Systems using Linear-fractional Representations and Linear Matrix Inequalities*

Introducation An optimization-based methodology for the multiobjective control of a large class of nonlinear systems is performed. The System Consider a nonlinear, continuous-time system where is the state vector, is the input and is the output. The Data is the state vector, is the input and is the output. are multivariable functions of x. (that is, 0 is an equilibrium point of the unforced system associated with the system). and have no singularities at the origin. Proof = + For a given scalar \sigma > 0, we associate with the Linear differential inclusion, The LMI: Control of Rational Systems using Linear-fractional Representations and Linear Matrix Inequalities For given \sigma > 0, the LDI system is quadratically stable if there exists P, S, and G such that the LMIs hold. Then, for every such that < 0 Conclusion The above LMIs provide a unified setting, as well as an efficient computational procedure, for answering (possibly conservatively) several control problems pertaining to a quite generic class of nonlinear systems. This method makes an explicit and systematic connection (via LFRs and LMIs) between robust control methods and nonlinear systems.