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New stability tests for positive descriptor linear systems

Kaczorek Tadeusz

Bulletin of the Polish Academy of Sciences. Technical Sciences

2022

Vol. 70, nr 3

art. no. e140688

The asymptotic stability of positive descriptor continuous-time and discrete-time linear systems is considered. New sufficient conditions for stability of positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of continuous-time and discrete-time linear systems.

Singular extremals in multi-input time-optimal problems: a sufficient condition

Chittaro F. C., Stefani G.

Control and Cybernetics

2010

Vol. 39, no 4

1029-1068

In this paper we study second order sufficient conditions for the strong-local optimality of singular Pontryagin extremals. In particular, we focus on the minimum-time problem for a control-affine system with vector inputs. We use Hamiltonian methods to prove that the coercivity of a suitably-defined second variation - plus an involutivity assumption on the distribution of the controlled fields - is a sufficient condition for the strong optimality of a candidate extremal.