Reduced realizations and model reduction for switched linear systems: a time-varying approach

In the last decades, switched systems gained much interest as a modeling framework in many applications. Due to a large number of subsystems and their high-dimensional dynamics, such systems result in high complexity and challenges. This motivates to find suitable reduction methods that produce simplified models which can be used in simulation and optimization instead of the original (large) system. In general, the study aims to find a reduced model for a given switched system with a fixed switching signal and known mode sequence. This thesis concerns first the reduced realization of switched systems with known mode sequence which has the same input-output behavior as original switched systems. It is conjectured that the proposed reduced system has the smallest order for almost all switching time duration. Secondly, a model reduction method is proposed for switched systems with known switching signals which provide a good model with suitable thresholds for the given switched system. The quantitative information for each mode is carried out by defining suitable Gramians and, these Gramians are exploited at the midpoint of the given switching time duration. Finally, balanced truncation leads to a modewise reduction. Later, a model reduction method for switched differential-algebraic equations in continuous time is proposed. Thereto, a switched linear system with jumps and impulses is constructed which has the identical input-output behavior as original systems. Finally, a model reduction approach for singular linear switched systems in discrete time is studied. The choice of initial/final values of the reachability and observability Gramians are also investigated.