Time response bounds for linear uncertain systems

Determination of a bounded compact set in parameter space for regional stability in the complex plane for linear uncertain systems has been an active topic of research. Several measures found so far in literature preserve migration of perturbed eigenvalues within the subregions of interest over these compact sets in the parameter space. However, in the majority of control problems, it is of interest to bound the time response in the presence of uncertain parameter variations. In this paper, the authors combine the eigenvalue and eigenvector perturbation analysis to propose a `tube´ about the nominal (desired) time response. If x(e_i)(t) and xi(t) are the i-th perturbed and nominal coordinates (either state or control variable) for a linear uncertain system, this paper establishes the bound ε_i(t) satisfying |x(e_i)(t)-x_i(t)|⩽ε_i(t) over the bounded parameter set. Here, ε_i(t) includes zero-input or zero-state response bounds