ℋ∞ and ℋ2 control design for polytopic continuous-time Markov jump linear systems with uncertain transition rates

摘要: Summary This paper investigates the problems of  and  state feedback control design for continuous-time Markov jump linear systems. The matrices each operation mode are supposed to be uncertain, belonging a polytope, and transition rate matrix is considered partly known. By appropriately modeling all uncertain parameters in terms multi-simplex domain, new conditions proposed, whose main advantage with respect existing ones allow use polynomially parameter-dependent Lyapunov certify mean square closed-loop stability. Synthesis derived inequalities scalar parameter. conditions, which become LMIs fixed values scalar, can cope both mode-independent mode-dependent cases. Using polynomial larger degrees performing search parameter, less conservative results guaranteed costs obtained through LMI relaxations. Numerical examples illustrate advantages proposed when compared other techniques from literature. Copyright © 2015 John Wiley & Sons, Ltd.