Robust stability and performance analysis of discrete-time piecewise affine systems with disturbances

For discrete-time piecewise affine systems, exponential stability and quadratic performance are analyzed in the presence of disturbances. Our approach is based on constructing a sequence of finite-state symbolic models for the piecewise affine system and analyzing the robust stability and performance of any of these symbolic models using linear matrix inequalities. The presented analysis is scalable; that is, the stability region or performance bound obtained by analyzing a symbolic model in the sequence is enlarged or improved, respectively, by analyzing the next symbolic model within the same sequence. Moreover, if the sequence turns out to be finite, then the last symbolic model in the sequence yields exact analysis of robust stability and performance.