Robust Control Problem for Nonstandard Singularly Perturbed Systems Under Perfect State Measurements

This paper considers the robust control problem for nonstandard singularly perturbed systems with time-varying norm-bounded parameter uncertainties in state equations. In order to obtain the controller such that both robust stability and a disturbance attenuation level larger than a arbitrary boundary value are achieved, irrespective of uncertainties, we must solve algebraic Riccati equation with the singular perturbation parameter > 0. The main results in this paper are to propose a new recursive algorithm to solve the above equation and to find an independent sufficient conditions for the existence of the full-order dynamic controller. Using the algebraic equation approach, although the uncertain matrix + has unstable mode, our new results are applicable to both standard and nonstandard uncertain singularly perturbed systems. Furthermore, in order to show the effectiveness of the proposed algorithms, numerical examples are included.