On the existence of common quadratic Lyapunov functions for second‐order linear time‐invariant discrete‐time systems

Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function (CQLF) are given for two second-order linear time-invariant discrete-time systems. These conditions are later extended to an arbitrary number of systems. The conditions are readily verifiable both analytically and graphically. The paper also provides a constructive procedure for computing a CQLF when it exists. Copyright © 2002 John Wiley & Sons, Ltd.