New approach to delay-dependent<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si0018.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math>control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions

This paper proposes an input–output (IO) approach to the delay-dependent stability analysis and H ∞ controller synthesis for a class of continuous-time Markovian jump linear systems (MJLSs). The concerned systems are with a time-varying delay in the state and deficient mode information in the Markov stochastic process, which simultaneously involves the exactly known, partially unknown and uncertain transition rates. It is first shown that the original system with time-varying delay can be reformulated by a new IO model through a process of two-term approximation and the stability problem of the original system can be transformed into the scaled small gain (SSG) problem of the IO model. Then, based on a Markovian Lyapunov–Krasovskii formulation of SSG condition together with some convexification techniques, the stability analysis and state-feedback H ∞ controller synthesis conditions for the underlying MJLSs are formulated in terms of linear matrix inequalities. Simulation studies are provided to illustrate the effectiveness and superiority of the proposed analysis and design methods.