Graded approximations and controllability along a trajectory
SIAM Journal on Control and Optimization
Stability Analysis of Second-Order Switched Homogeneous Systems
SIAM Journal on Control and Optimization
An Elementary Counterexample to the Finiteness Conjecture
SIAM Journal on Matrix Analysis and Applications
Structure of extremal trajectories of discrete linear systems and the finiteness conjecture
Automation and Remote Control
Brief paper: Root-mean-square gains of switched linear systems: A variational approach
Automatica (Journal of IFAC)
Bilinear Control Systems: Matrices in Action
Bilinear Control Systems: Matrices in Action
Stability analysis of switched systems using variational principles: An introduction
Automatica (Journal of IFAC)
Absolute stability of third-order systems: A numerical algorithm
Automatica (Journal of IFAC)
Optimal control of switching systems
Automatica (Journal of IFAC)
Brief paper: Controllability of Boolean control networks via the Perron-Frobenius theory
Automatica (Journal of IFAC)
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A powerful approach for analyzing the stability of continuous-time switched systems is based on using tools from optimal control theory to characterize the “most unstable” switching law. This reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific “most unstable” switching law. More generally, this so-called variational approach was successfully applied to derive nice-reachability-type results for both linear and nonlinear continuous-time switched systems. Motivated by this, we develop in this paper an analogous approach for discrete-time linear switched systems. We derive and prove a necessary condition for optimality of the “most unstable” switching law. This yields a type of discrete-time maximum principle (MP). We demonstrate by an example that this MP is in fact weaker than its continuous-time counterpart. To overcome this, we introduce the auxiliary system of a discrete-time linear switched system and show that regularity properties of time-optimal controls for the auxiliary system imply nice-reachability results for the original discrete-time linear switched system. Using this approach, we derive several new Lie-algebraic conditions guaranteeing nice-reachability results. These results, and their proofs, turn out to be quite different from their continuous-time counterparts.