This paper addresses the stabilisation of discrete-time switching linear systems (DTSSs) with control inputs under arbitrary switching, based on the existence of a common quadratic Lyapunov function (CQLF). The authors have begun a line of work dealing with control design based on the Lie-algebraic solvability property. The present paper expands on earlier work by deriving sufficient conditions...

In this paper we consider the class of discretetime systems switching between an arbitrary number p of autonomous positive subsystems. Necessary and sufficient conditions for the existence of (either linear or quadratic) copositive Lyapunov functions, whose values can be decreased in every positive state, by suitably choosing one of p subsystems, are obtained. When these conditions are fulfille...

An integrated design of switching laws and feedback controllers for uncertain switched nonlinear control-affine systems with an arbitrary number of subsystems is developed. Sufficient conditions for the existence of globally asymptotically stabilizing state feedback laws are derived using the control Lyapunov function approach. Additionally, an explicit rule for constructing switching laws and ...

The potential of a χ photonics, implemented in periodically poled Lithium Niobate (PPLN) waveguides with an engineerable quadratic nonlinearity, for ultrafast all-optical signal routing and switching will be evaluated. High bit rate signal regeneration and routing, based on spatial soliton formation in film waveguides, as well as transparent switching, based on parametric amplification in waveg...

The switching signal design for global exponential stability of switched neutral systems is investigated in this paper. LMI-based delay-dependent and delay-independent criteria are proposed to guarantee the global stability via the constructed switching signal. Razumikhin-like approach is used to find the stability results. Finally, some numerical examples are illustrated to show the main results.

By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. This article surveys recent developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching...

Stability of periodic switched linear systems with fast switching patterns is studied by combining the method of averaging with exponential splitting. This approach yields less conservative bounds on stabilizing fast switching rates than can be obtained with prior approaches. Such bounds can be useful for analysis and design of switching control laws. The method is also generalized to arbitrary...

We study a switching synchronization phenomenon taking place in one-dimensional memristive networks when the memristors switch from the high to low resistance state. It is assumed that the distributions of threshold voltages and switching rates of memristors are arbitrary. Using the Laplace transform, a set of non-linear equations describing the memristors dynamics is solved exactly, without an...

The paper deals with the realization theory of linear and bilinear switched systems. Necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a (bi)linear switched system. Characterization of minimal realizations is presented. The paper treats two types of (bi)linear switched systems. The first one is when all switching sequences are allowed. The ...