Controllability and reachability criteria for switched linear systems

Abstract

This paper investigates the controllability and reachability of switched linear control systems. It is proven that both the controllable and reachable sets are subspaces of the total space. Complete geometric characterization for both sets is presented. The switching control design problem is also addressed.

Switching Stabilizability for Continuous-Time Uncertain Switched Linear Systems

“…Properties of this type of model have been studied for the past fifty years to consider engineering systems that contain relays and/or hysteresis. Due to its success in application and importance in theory, the last decade has seen increasing research activities in stability [8], [19], [22], controllability [34], [35], observability [1], [10], [14], stabilization [16], [25], [33], and switching optimal control [2], [39] of switched systems.…”

Structural Observability of Controlled Switching Linear Systems

“…As to arbitrarily switched linear systems, Sun and Zheng [21] first gave a sufficient condition and a necessary condition for controllability and proved that the necessary condition is also sufficient fo r three-d imensional systems with on ly two subsystems. Following the work in [21] and [22] extended the result to three-dimensional systems with arbit rary number o f subsystems. Then, necessary and sufficient geometric type criteria for controllability and observability were derived in [22] and [7].…”

Rank tests for the observability of discrete-time jump linear systems with inputs

“…Among the existing works on observability of discrete-time JLSs, the ones that are more closely related to our approach are [1], [3], [4], [2]. In comparison to the work of [3], the main contribution of this paper is that the switching sequence is viewed as an unknown parameter which needs to be estimated, rather than as a measured input. With respect to the work of [4] on observability of autonomous JSLs, the main contribution of our work is to consider more general definitions of observability for JLSs with inputs.…”

“…[10] gives conditions for the observability of a particular class of linear time-varying systems where the system matrix is a linear combination of a basis with respect to time-varying coefficients. [3] gives a condition for the observability of switched linear systems where the switching is assumed to be a measured input. [11] gives conditions for observability of bilinear and linear hybrid systems in continuous time, where the discrete states change according to a finite automaton and the discrete events are measured external inputs.…”