Stabilization of polytopic delay difference inclusions: Time-varying control Lyapunov functions

This paper studies stabilization of polytopic delay difference inclusions via the Razumikhin approach. An example of a linear delay difference equation that is globally exponentially stable (GES) but does not admit a standard LyapunovRazumikhin function (LRF) is presented. Motivated by this shortcoming, time-varying Lyapunov functions are proposed as a tool for stability analysis of time-delay systems. It is shown that any polytopic delay difference inclusion that is GES admits a quadratic time-varying Lyapunov-Krasovskii function and, under an additional mild assumption, it also admits a quadratic time-varying LRF. These results are further exploited to derive a stabilizing receding horizon control scheme for time-delay systems that does not suffer from an exponential increase in complexity when the size of the delay increases. The proposed control scheme requires solving on-line a single semi-definite program.

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Rob H. Gielen, Mircea Lazar
• Keywords: CDC 2010, Control Systems, Delay Difference, Delay Difference Inclusion, Polytopic Delay Difference