Abstract
This paper studies the static output quadratic control problem of discrete-time Markov jump linear systems (MJLS) with hard constraints on the norm of the state and control variables. Both cases the finite horizon as well as the infinite horizon are considered. Regarding the Markov chain parameter $\theta (k)$ , it is assumed that the controller only has access to a detector which emits signals $\widehat {\theta }(k)$ providing information on the parameter $\theta (k)$ . The goal is to design a static output feedback linear control using the information provided by detector $\widehat {\theta }(k)$ in order to minimize an upper bound for the quadratic cost and satisfy the hard constraints. For the infinite horizon case it is also imposed that the controller stochastically stabilizes the closed loop system. LMIs (linear matrix inequalities) are formulated in order to obtain a solution for these optimization problems. The cases in which the initial conditions are fixed and when it is desired to maximize an estimate of the domain of an invariant set are also analyzed. Some numerical examples are presented for the purpose of illustrating the results obtained.
Highlights
In recent years systems subject to sudden changes in their dynamics have been the focus of many researches in engineering and related fields
We can find in the literature several works using this framework, referred to as asynchronous control as presented, e.g., in Song et al [34], [35], in which the problems of static output feedback control and sliding mode control of Markov jump linear systems (MJLS) with hidden observations were considered, and Dong et al [12]–[14], where an asynchronous
This paper deals with constrained static output control for discrete-time MJLS with partial information using LMI optimization problems for minimizing an upper bound for the quadratic cost function and/or maximizing the estimate of the domain of an invariant set with a fixed upper bound cost
Summary
In recent years systems subject to sudden changes in their dynamics have been the focus of many researches in engineering and related fields. From [5], [21], [25], [40], [42], [43], we introduce the constrained quadratic control for discrete-time MJLS considering that the Markov parameter θ (k) is not available to the controller and, instead, we only have an estimation for this parameter provided by θ(k) with an associated detection probability matrix, following the hidden MJLS methodology.
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