Another key issue of the LPV system is to construct parameter-dependent Lyapunov functions to overcome potential conservatism brought by the slowly varying parameters.
Arzelier, "Robust performance analysis with LMI-based methods for real parametric uncertainty via parameter-dependent Lyapunov functions," IEEE Transactions on Automatic Control, vol.
Indeed, less conservative robust stability conditions are given by means of a parameter-dependent Lyapunov function and a slack method for exploiting the algebraic properties of the uncertain Roesser-type discrete-time 2D system (1).
Consider the following parameter-dependent Lyapunov function which is suitable for the uncertain Roesser-type discrete-time 2D system (1):
Then, the variation of the parameter-dependent Lyapunov function V(x(k, l)) could be described as
Indeed, the parameter-dependent Lyapunov function V(x(k, l)) = [x.sup.T](k, l)[P.sub.[alpha][alpha]]x(k, l) is applied in the derivation of our main result and thus the obtained robust stability criteria are less conservative than before.
The problem of robust stability analysis of a class of uncertain Roesser-type discrete-time 2D systems has been addressed by using an efficient parameter-dependent Lyapunov function. In particular, the parameter uncertainties of the underlying 2D system's parameter matrices belong to a convex bounded uncertain domain, which often is named as polytopic uncertainty and appears typically in most practical systems.