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Abstract: This paper deals with quadratic stability and feedback stabilization problems for continuous bimodal piecewise linear systems. First, we provide necessary and sufficient conditions in terms of linear matrix inequalities for quadratic stability and stabilization of this class of systems. Later, these conditions are investigated from a geometric control point of view and a set of sufficient conditions (in terms of the zero dynamics of one of the two linear subsystems) for feedback stabilization are obtained. [Copyright &y& Elsevier]

This paper investigates semistability and its computation for discrete-time, switched linear systems under both deterministic and random switching policies. The notion of semistability pertains to a continuum of initial state dependent equilibria, and finds wide applications in multi-agent and distributed network systems. It is shown in this paper that exponential semistability on a common equilibrium space is equivalent to output exponential stability of a reduced switched linear system with a suitably defined output, under arbitrary and random switchings. Besides, their convergence rates are shown to be identical. A generating function based approach is proposed to compute convergence rates of the reduced switched systems under these switching rules. The obtained semistability results are applied to performance analysis of PageRank algorithms for distributed web-page systems subject to topology switching. The iteration processes of these algorithms are formulated as switched linear systems. Their equilibrium properties are studied, and convergence rates are characterized via the semistability techniques and the generating function approach. [ABSTRACT FROM AUTHOR]

Abstract: Belonging to the broad framework of hybrid systems, conewise linear systems (CLSs) form a class of Lipschitz piecewise linear systems subject to state triggered mode switchings. Motivated by state estimation of nonsmooth switched systems, this paper exploits directional derivative and positive invariance techniques to characterize finite-time and long-time local observability of a general CLS. For the former observability notion, directional derivative results are developed from the simple switching property, and they yield improved observability conditions. For the latter notion, we focus on the case where a nominal trajectory has finitely many switchings. In order to characterize long-time behaviors of the CLS, necessary and sufficient conditions are obtained for the interior of a positively invariant cone. By employing these conditions, we establish connections between finite-time and long-time local observability; underlying positive invariance properties are unveiled. [Copyright &y& Elsevier]