Partial boundedness analysis: a state-space transformation method for reshaping the estimated domain of stability

This study focuses on the problem of the state upper bound estimation for linear systems subject to amplitude-bounded disturbances. A state-space transformation method is proposed to reshape the estimated domain of stability, which is used to analyse the upper bound of a part of system states. By analysing the estimated domains of stability corresponding to different quadratic Lyapunov functions (QLFs), a universal expression for the upper bounds of a part of system states is obtained. By minimising the universal expression, an appropriate QLF is designed to gain the less conservative estimation on the upper bound of a part of system states. The proposed method provides a novel way of constructing and selecting the appropriate QLF to obtain the less conservative results on the upper bound of a part of system states. The effectiveness of the method is illustrated by two examples.