A time-varying Gramian based model reduction approach for Linear Switched Systems

Minimality of Linear Switched Systems with known switching signal

“…x q (t + q ) = J σ(t + q ),σ(t − q ) x q−1 (t − q ), y(t) = C σ(t) x q (t), t ∈ R, (1) where x q : (t q , t q+1 ) → R nq is the absolutely continuous q-th piece of the state, u : R → R u is the input and y is the measured output. The switching signal σ : R → Q = {1, 2, • • • , f } ⊂ N is a given piecewise constant function with finitely many switching times:…”

“…In particular, finding a minimal realization could be seen as the first step towards model reduction. In [1], we have presented a time-varying model reduction approach for linear switched system which was not a switched system anymore. Therefore, our aim is to gain insight into a more suitable model-reduction approach by studying the minimal realization problem for switched systems of the form (1) within this system class.…”

“…Several approaches have been discussed in the cases of arbitrary and constrained switching e.g. in [1][2][3][4][5] where switching signal are viewed as input to the switched systems. It can be seen that (minimal) realization in general depends on the specifically given switching signal, so in contrast to the existing literature, we view the switched system (1) as a piecewiseconstant time-varying linear system.…”

“…The above definition of minimality is not specifying any method to obtain a minimal realization from a given switched system as in (1). In general, a minimal realization can only be obtained by considering each mode individually (and by properly taking the effect on the other modes into account).…”

Reduced realizations and model reduction for switched linear systems

“…A brief version of Chapter 4 will be presented at the 10th International Conference on Mathematical Modelling (MATHMOD 2022) in Vienna, Austria, and this chapter has also been submitted for journal publication. A brief version of Chapter 5 has been presented at IFAC World Congress 2020 and published as [58]. Chapter 6 has been submitted for journal publication.…”