Related papers: Explicit Commutativity Conditions for Second-order…
After reviewing commutativity of second-order linear time-varying analog systems, the inverse commutativity conditions are derived for these systems by considering non-zero initial conditions. On the base of these conditions, the…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
After introducing the concept of commutativity for continuous-time linear time-varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete-time linear…
Decomposition is a common tool for synthesis of many physical systems. It is also used for analyzing large scale systems which then known as tearing and reconstruction. On the other hand, commutativity of cascade connected systems have…
In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
We propose matrix commutator based stability characterization for discrete-time switched linear systems under restricted switching. Given an admissible minimum dwell time, we identify sufficient conditions on subsystems such that a switched…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of…
In this paper, existence conditions and a design procedure of reduced-order switched positive observers for continuous- and discrete-time switched positive linear systems with uncertainty are established. In the analyzed class, arbitrary…
We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those…
We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on…
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…
We derive sufficient conditions for the solvability of the observer design problem for a wide class of nonlinear time-varying systems, including those having triangular structure. We establish that, under weaker assumptions than those…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification. This condition generalizes the so-called linear independence constraint qualification.…