Measurable disturbance rejection with stability in continuous-time switched linear systems under dwell-time switching

Abstract

This work deals with rejection of disturbance inputs accessible for measurement in continuous-time switched linear systems with dwell-time constraints on the switching signals. The measurable disturbance rejection problem is stated as the problem of finding a dynamic feedforward switched compensator achieving zero output and exponential stability of the compensated switched linear system over a class of switching signals with a sufficiently large dwell-time, in the presence of any admissible measurable disturbance input. The synthesis of the compensator is based on a pair of sufficient conditions which respectively address the structural issue and the stabilizability issue. The former condition is expressed in geometric terms as the inclusion of the image of the disturbance input matrix in the sum of the so-called maximal robust controlled invariant subspace and the image of the control input matrix, for all the modes of the given switched system. The second condition is expressed as the exponential stabilizability under dwell-time switching of the internal switched dynamics of the maximal robust controlled invariant subspace.

A geometric approach to structural model matching by output feedback in linear impulsive systems

“…), it is preferred herein to refer to the notions introduced in some of our previous papers (e.g., Zattoni et al, 2017b), since they address linear impulsive systems with the same characteristics as those considered herein. On a last note, it is worth mentioning that the geometric approach has proven to be very effective also in mastering control problems stated for other classes of hybrid systems, such as switched linear systems Zattoni, 2014;Conte et al, 2013;Zattoni and Marro, 2013b).…”

Disturbance Decoupling With Stability in Discrete-Time Switching Linear Systems: Arbitrary Switching

“…Disturbance decoupling has been studied for various other classes of dynamical systems and, because of the peculiarities arising in each context, it still attracts the interest of the research community. Indeed, disturbance decoupling has recently been considered for nonlinear systems [7], descriptor systems and systems over rings [8], time-delay systems [9,10], linear parameter varying systems [11,12], hybrid linear systems with state jumps [13,14], and switching linear systems [15,16,17,18,19,20,21,22,23,24,25,26,27]. The motivation for investigating possible solutions of the disturbance decoupling problem for more general classes of dynamical systems than linear time-invariant systems is not only the intrinsic theoretic interest of finding relaxed solvability conditions, but also the need to find powerful tools to solve more intricate problems like, for instance, model matching [28,29,30,31].…”

“…In [23,16] both the switching signal and the control input are to be designed so as to achieve decoupling of the exogenous disturbance. In [18,19,20,21,22,24,25,26,27], the manipulable variable is the control input, but the switching signal is assumed to be measurablehence, available to the compensator.…”

“…In [18,19,20,24,25], quadratic stability is required for all the switching signals satisfying the only constraint that the number of switches they cause is finite in any finite time interval. In [21,22,26,27], asymptotic stability is demanded for all the switching signals in a class characterized by a minimum dwell-time.…”

“…In [21,22,26,27], the switching signals are assumed to be subject to a constraint on the minimum dwell-time: i.e., the length of the time interval between two consecutive switches must be greater than or equal to a positive real constant. In [18,19,20,24,25], the admissible switching signals are assumed to be arbitrary, under the only provision that the number of switches in any finite time interval is finite, so as to avoid possible Zeno behaviors.…”