Nonlinear Systems Evolving with State Suprema as Multi-Mode Multi-Dimensional (M3D) Systems: Analysis & Observation

This paper considers the class of systems described by functional differential equations involving the sup-operator. This feature makes these systems infinite dimensional and nonlinear. We consider the general higher order case where the partial state, x(t), lies in Rn. The state space for such systems is an infinite-dimensional Banach space equipped with the uniform convergence topology. We elucidate that such systems may be modeled as Multi-Mode Multi-Dimensional (M3D) systems. The stability and observer design for such systems is studied, the first using Razumikhin's framework, the second using the new concept of sup based output injection. Simulation results are shown at the end which demonstrate the effectiveness, validity and usefulness of the proposed observer scheme.