Pseudo-linear systems, Lie algebras, and stability

Differential Invariant Algebras of Lie Pseudo–Groups

The goal of this paper is to describe, in as much detail as possible, the structure of the algebra of differential invariants of a Lie pseudo-group. Under the assumption of local freeness of the prolonged pseudo-group action, we develop algorithms for locating a finite generating set of differential invariants, establishing the recurrence relations for the differentiated invariants, and fixing ...

Lie Algebras and their corresponding linear groups

Pseudo Linear Systems: Stability Analysis and Limit Cycle Emergence

Nonlinear autonomous systems, often arise in different fields of science, are usually difficult to analyze. Pseudo linear representation of such systems recently has become very popular to deal with this difficulty. This paper presents a deep through analysis about the stability of nonlinear autonomous systems represented by pseudo linear forms. By discretization of the continuous-time dynamica...

Lie $^*$-double derivations on Lie $C^*$-algebras

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

On robust Lie-algebraic stability conditions for switched linear systems

This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system paramete...