(2015) Morais, Cecilia de Freitas; Braga, Marcio Feliciano; Oliveira, Ricardo Coração de Leão Fontoura de; Peres, Pedro Luis Dias
This paper investigates the problems of H1 and H2 state feedback control design for continuous-time
Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging
to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all
the uncertain parameters in terms of a multi-simplex domain, new design conditions are proposed, whose
main advantage with respect to the existing ones is to allow the use of polynomially parameter-dependent
Lyapunov matrices to certify the mean square closed-loop stability. Synthesis conditions are derived in
terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values
of the scalar, can cope with H1 and H2 state feedback control in both mode-independent and modedependent
cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for
the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI
relaxations. Numerical examples illustrate the advantages of the proposed conditions when compared with
other techniques from the literature.
