Research ArticleL1/ℓ1-Gain analysis and synthesis of Markovian jump positive systems with time delay

- The concept of stochastic stability with L1/ℓ1-gain is introduced.
- Sufficient conditions for the stochastic stability with L1/ℓ1-gain are established.
- State-feedback control laws are designed to ensure the stochastic stability.

This paper is concerned with stability analysis and control synthesis of Markovian jump positive systems with time delay. The notions of stochastic stability with L1- and ℓ1-gain performances are introduced for continuous- and discrete-time contexts, respectively. Using a stochastic copositive Lyapunov function, sufficient conditions for the stability with L1/ℓ1-gain performance of the systems are established. Furthermore, mode-dependent controllers are designed to achieve the stabilization with L1/ℓ1-gain of the resulting closed-loop systems. All proposed conditions are formulated in terms of linear programming. Numerical examples are provided to verify the effectiveness of the findings of theory.