Stability and performance analysis of time delayed linear parameter varying systems with brief instability

LPV systems provide a systematic framework for the study of nonlinear systems by analyzing a representative family of linear time-invariant systems parameterized by some system parameters residing in compact set. The brief instability concept in such systems allows the linear system to be unstable for some values of the LPV parameters so that instability occurs only for short periods of time. The present paper extends the notion of brief instability to LPV systems with time delay in their dynamics. It provides tools for the stability and performance analysis of these systems, where performance is evaluated in terms of induced L₂-gain (or so-called H^infin norm). The main results of the paper illustrate that stability and performance conditions can be evaluated by examining the feasibility of parameterized sets of Linear Matrix Inequalities (LMIs). As an application of the derived analysis formulation, we use the interconnection of an LPV time delay system and a parameter-varying observer to estimate the outputs of the delayed system. The temporary loss of information arriving from sensors is taken into account to represent brief instability in the system. The numerical examples are used to illustrate the qualifications of the proposed analysis and synthesis conditions for loss of sensor data.