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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]

We consider planar bilinear control systems with measurable controls. We show that any point in the reachable set can be reached by a "nice" control, specifically, a control that is a concatenation of a bang arc with either 1) a bang-bang control that is periodic after the third switch; or 2) a piecewise constant control with no more than two discontinuities. Under the additional assumption that the bilinear system is positive (or in- variant for any proper cone), we show that the reachable set is spanned by a concatenation of a bang arc with either 1) a bang-bang control with no more than two discontinuities; or 2) a piecewise constant control with no more than two discontinuities. In particular, any point in the reachable set can be reached using a piecewise-constant control with no more than three discontinuities. Several known results on the stability of planar linear switched systems under arbitrary switching follow as corollaries of our result. We demonstrate this with an example. [ABSTRACT FROM AUTHOR]

Abstract-For a group of linear systems, each under a saturated linear, not necessarily stabilizing, feedback law, we design a switching scheme such that the resulting switched system is locally asymptotically stable at the origin with a large domain of attraction. By expressing each saturated linear feedback in a convex hull of a group of auxiliary linear feedbacks, we formulate and solve the problem of designing such a switching scheme as a constrained optimization problem with the objective of maximizing an estimate of the domain of attraction. Simulation results indicate that the resulting domain of attraction extends well beyond the linear regions of the actuators. [ABSTRACT FROM AUTHOR]

This paper investigates the number of switchings and design of switching sequences for controllability of switched linear systems. Two related results are established. One is a new constructive approach to designing switching sequences. The controllable state set of each switching sequence designed via the approach coincides with the controllable subspace of switched linear systems. The other is a well-estimated value for the minimum number of switchings required for controllability. Each state in the controllable subspace can be steered to origin within this value of switching times. [ABSTRACT FROM AUTHOR]

We consider products of matrix exponentials under the assumption that the matrices span a nilpotent Lie algebra. In 1995, Gurvits conjectured that nilpotency implies that these products are, in some sense, simple. More precisely, there exists a uniform bound l such that any product can be represented as a product of no more than l matrix exponentials. This conjecture has important applications in the analysis of linear switched systems, as it is closely related to the problem of reachability using a uniformly bounded number of switches. It is also closely related to the concept of nice reachability for bilinear control systems. The conjecture is trivially true for the case of first-order nilpotency. Gurvits proved the conjecture for the case of second-order nilpotency using the Baker-Campbell-Hausdorff formula. We show that the conjecture is false for the third-order nilpotent case using an explicit counterexample. Yet, the underlying philosophy behind Gurvits' conjecture is valid in the case of third-order nilpotency. Namely, such systems do satisfy the following nice reachability property: any point in the reachable set can be reached using a piecewise constant control with no more than four switches. We show that even this form of finite reachability is no longer true for the case of fifth-order nilpotency. [ABSTRACT FROM AUTHOR]

It was recently conjectured that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching. In this note, we show that 1) this conjecture is true for systems constructed from a pair of second-order Metzler matrices; 2) the conjecture is true for systems constructed from an arbitrary finite number of second-order Metzler matrices; and 3) the conjecture is in general false for higher order systems. The implications of our results, both for the design of switched positive linear systems, and for research directions that arise as a result of our work, are discussed toward the end of the note. [ABSTRACT FROM AUTHOR]

This paper investigates the switching stabilizability problem for a class of continuous-time switched linear systems with time-variant parametric uncertainties. First, a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived, under the assumption that the closed-loop switched system does not generate sliding motions. Then, an additional condition is introduced to exclude the possibility of unstable sliding motions. Finally, a necessary and sufficient for the asymptotic stabilizability of such continuous-time uncertain switched linear systems is presented. This result improves upon conditions found in the literature which are either sufficient only or necessary only. [ABSTRACT FROM AUTHOR]

We consider continuous time switched systems that are stabilized via a computer. Several factors (sampling, computer computation, communications through a network, etc.) introduce model uncertainties produced by unknown varying feedback delays. These uncertainties can lead to instability when they are not taken into account. Our goal is to construct a switched digital control for continuous time switched systems that is robust to the varying feedback delay problem. The main contribution of this note is to show that the control synthesis problem in the context of un- known time varying delays can be expressed as a problem of stabilizability for uncertain systems with polytopic uncertainties. [ABSTRACT FROM AUTHOR]