Stability of Planar Switched Systems: The Linear Single Input Case
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
Complex Polytope Extremality Results for Families of Matrices
SIAM Journal on Matrix Analysis and Applications
Structure of extremal trajectories of discrete linear systems and the finiteness conjecture
Automation and Remote Control
Counterexamples to the Complex Polytope Extremality Conjecture
SIAM Journal on Matrix Analysis and Applications
Finding Extremal Complex Polytope Norms for Families of Real Matrices
SIAM Journal on Matrix Analysis and Applications
Stability analysis of switched systems using variational principles: An introduction
Automatica (Journal of IFAC)
Analysis of Discrete-Time Linear Switched Systems: A Variational Approach
SIAM Journal on Control and Optimization
Hi-index | 22.14 |
We consider the stability under arbitrary switching of a discrete-time linear switched system. A powerful approach for addressing this problem is based on studying the ''most unstable'' switching law (MUSL). If the solution of the switched system corresponding to the MUSL converges to the origin, then the switched system is stable for any switching law. The MUSL can be characterized using optimal control techniques. This variational approach leads to a Hamilton-Jacobi-Bellman equation describing the behavior of the switched system under the MUSL. The solution of this equation is sometimes referred to as a Barabanov norm of the switched system. Although the Barabanov norm was studied extensively, it seems that there are few examples where it was actually computed in closed-form. In this paper, we consider a special class of positive planar discrete-time linear switched systems and provide a closed-form expression for a corresponding Barabanov norm and a MUSL. The unit circle in this norm is a parallelogram.