DA and RDA in Non-polynomial Systems
This chapter presents the estimation of the DA of equilibrium for a class of non-polynomial systems, i.e. dynamical systems whose dynamics cannot be described by a polynomial function of the state. In particular, it is supposed that the dynamics is described by an affine combination of non-polynomial functions weighted by polynomials, where each non-polynomial function depends on a single entry of the state. It is shown that a condition for establishing whether a sublevel set of a LF is an estimate of the DA can be obtained in terms of LMI feasibility tests by introducing truncated Taylor expansions with worst-case remainders of the non-polynomial functions. These LMI feasibility tests are independent on each other and correspond to a combination of the bounds of the remainders. Then, the problem of computing the LEDA provided by a LF is addressed, showing that in general a candidate of such an estimate can be found by solving a certain number of GEVPs. A sufficient condition for establishing whether the found candidate is tight is hence provided by looking for power vectors in linear subspaces. Moreover, the computation of optimal estimates of the DA, the problem of establishing global asymptotical stability of the equilibrium point, and the design of polynomial static output controllers for enlarging the DA, are addressed. These problems require to consider simultaneously the systems of LMIs obtained for different combinations of the bounds of the remainders, which consequently have to be determined for an overestimate of the candidate sublevel set. Lastly, the proposed methodology is extended to a class of uncertain non-polynomial systems, in particular non-polynomial systems with coefficients depending polynomially on a time-invariant uncertain vector constrained over a semialgebraic set.
KeywordsEquilibrium Point Stir Tank Reactor Polynomial System Temporal Derivative Global Asymptotical Stability
Unable to display preview. Download preview PDF.