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Improving performance analysis with structures of outputs and constraints

This paper is devoted to the analysis of output performances for linear systems with state/output constraints. Analysis methods are obtained by incorporating the structures of outputs and state constraints into non-quadratic Lyapunov functions. Output ranges and overshoots are estimated for given sets of initial conditions and bounded inputs. Attempts are also made to detect a large invariant set within state/output constraints. Numerical examples demonstrate the effectiveness of the non-quadratic Lyapunov functions and the proposed methods. In particular, it is shown that, even for linear time invariant systems, the output bound can be sharpened by using a simple non-quadratic Lyapunov function that incorporates the structure of the output.