Search

A moment-matching method for model reduction of linear switched systems (LSSs) is presented. The method can be seen as a non-trivial extension of the Krylov subspace methods for linear time-invariant (LTI) systems. The procedure is based on the so called “nice selections,” which represent a choice of basis in the reachability or observability space of the LSS. The framework can also be used for exact matching of the input-output behavior of an LSS with a reduced order LSS for a specific switching sequence. Conditions for applicability of the method for model reduction are stated and finally the results are illustrated on numerical examples. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the derivation of a model reference adaptive control (MRAC) scheme for multimodal piecewise-affine (PWA) and piecewise-linear systems. The control allows the plant to track asymptotically the states of a multimodal piecewise affine (or smooth) reference model. The reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant. Numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability. [ABSTRACT FROM AUTHOR]

In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques. [ABSTRACT FROM PUBLISHER]

Two state observers are designed for some classes of switched linear systems with unknown inputs. The design of the proposed observers assumes that all switching subsystems fulfill a property of “strong detectability” refid="ref4"/ that allows to implement suitable reduced-order unknown-input switched observers. The synthesis of the observers is based on the feasibility of a certain system of LMIs. Two main schemes are presented. For the case when the set of possible unknown-input distribution matrices are linearly dependent, an observer is suggested that guarantees the asymptotic state reconstruction without imposing any slow-switching dwell-time constraint about the sequence of the switching times. For the general case, the existence of a minimal average dwell-time for every switching sequence is assumed. By appropriate Lyapunov analysis, the convergence of the state estimate is proven to be exponential in both cases. Simulation results confirm the predicted performance. [ABSTRACT FROM AUTHOR]

This technical note presents a regulator synthesis approach for switched bimodal linear systems where it is desired to achieve regulation against known disturbance or reference signals. First, a set of observer-based Q-parameterized stabilizing controllers for the switched system is constructed. Then regulation conditions for the switched system are obtained and a regulator synthesis method is derived based on iteratively solving a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We consider n-dimensional positive linear switched systems. A necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is Hurwitz. Several researchers conjectured that for positive linear switched systems this condition is also sufficient. Recently, Gurvits, Shorten, and Mason showed that this conjecture is true for the case n = 2, but is not true in general. Their results imply that there exists some minimal integer np, such that the conjecture is true for all n < np, but is not true for n = np. We show that np = 3. [ABSTRACT FROM AUTHOR]