Abstract
This paper considers the robust H∞ control problem for nonstandard singularly perturbed systems with time-varying norm-bounded parameter uncertainties in both state and output equations. In order to obtain the controller such that both robust stability and a disturbance attenuation level γ larger than a arbitrary boundary value are achieved, irrespective of uncertainties, we must solve two algebraic Riccati equations with the singular perturbation parameter ε>0. The main results in this paper are to propose a new algorithm to solve the above equations and to find an ε independent sufficient conditions for the existence of the full-order dynamic controller. Using the algebraic Riccati equation approach, although the uncertain matrix A22+ΔA22(t) 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.
