Article

# Stability of Planar Switched Systems: The Linear Single Input Case.

SIAM J. Control and Optimization 01/2002; 41:89-112. DOI: 10.1137/S0363012900382837

Source: DBLP

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**ABSTRACT:**Many practical systems can be modelled as switched systems, whose stability problem is challenging even for linear subsystems. In this article, the stability problem of second-order switched linear systems with a finite number of subsystems under arbitrary switching is investigated. Sufficient and necessary stability conditions are derived based on the worst-case analysis approach in polar coordinates. The key idea of this article is to partition the whole state space into several regions and reduce the stability analysis of all the subsystems to analysing one or two worst subsystems in each region. This article is an extension of the work for stability analysis of second-order switched linear systems with two subsystems under arbitrary switching.International Journal of Control - INT J CONTR. 01/2012; - [Show abstract] [Hide abstract]

**ABSTRACT:**This work is motivated by the drug therapy scheduling problem in HIV infection. Using simplified switched linear system models of HIV mutation and treatment with certain class of symmetry and finite horizon cost functions, we demonstrate that the optimal state and costate trajectories lie on a sliding surface where infinitely fast switching may occur. Results suggest that in the absence of other practical constraints, switching rapidly between therapies is relevant. Simulations show the potential benefits of a proactive switching strategy to minimize viral load and delay the emergence of resistant mutant viruses.Automatica (Journal of IFAC). 09/2013; 49(9):2874-2880. - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, the stabilizability of discrete-time linear switched systems is considered. Several sufficient conditions for stabilizability are proposed in the literature, but no necessary and sufficient. The main contributions are the necessary and sufficient conditions for stabilizability based on the set-theory and the characterization of a universal class of Lyapunov functions. An algorithm for computing the Lyapunov functions and a procedure to design the stabilizing switching control law are provided, based on such conditions. Moreover, a sufficient condition for non-stabilizability for switched system is presented. Several academic examples are given to illustrate the efficiency of the proposed results. In particular, a Lyapunov function is obtained for a system for which the Lyapunov–Metzler condition for stabilizability does not hold.Automatica. 01/2014; 50(1):75–83.

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