Robust degree of exponential stability in polynomially uncertain overlapping control systems

In this paper, necessary and sufficient conditions are provided for the existence of a structurally constrained controller in order to achieve a desired rate of exponential stability. It is assumed that a finite-dimensional linear time-invariant (LTI) system with uncertain parameters which belong to a known domain is given. The objective is to check if the poles of the closed-loop system can be placed in a desired region in the complex plane, for all values of the uncertain parameters in the known domain of uncertainty. The problem is investigated in both cases of LTI and linear time-varying (LTV) control laws. The results can be very useful in the design of overlapping control systems, when it is desired to maintain a prescribed transient performance for all permissible values of the uncertain parameters. The efficacy of the proposed technique is demonstrated by an example.