Stochastic stabilization and induced ℓ2ℓ2-gain for discrete-time Markov jump Lur’e systems with control saturation

This paper addresses the problem of control synthesis for locally stabilizing and minimizing the finite ℓ2ℓ2 gain for discrete-time Markov jump Lur’e systems with control saturation and exogenous ℓ2ℓ2-type disturbance. We consider that the jump parameter defining the active mode for both the linear and the cone-bounded nonlinearity is governed by a finite state homogeneous Markov chain. The local stochastic stability is established by exploiting the invariant probability measure of the Markov chain to define the level set of the expected value of the stochastic Lur’e type Lyapunov function. Optimization problems for maximizing our estimate of the domain of stochastic stability and minimizing the induced ℓ2ℓ2 gain with respect to exogenous disturbances are presented subject to LMI constraints. The paper is concluded with an academic example.