1c:I[419806,["/_next/static/chunks/bb923814e1f4d2e9.js","/_next/static/chunks/dd3ee9f5b7716ca6.js","/_next/static/chunks/4204a0ae82542ca8.js","/_next/static/chunks/1270dead247da766.js","/_next/static/chunks/6e1aa89a642f40be.js","/_next/static/chunks/2d7aa753e81324a8.js","/_next/static/chunks/8ffd0b71567920d8.js","/_next/static/chunks/67ea6dfd21f16c5f.js","/_next/static/chunks/24eb4379f68013fd.js","/_next/static/chunks/b8cd775ffdf935bd.js","/_next/static/chunks/983103cd9eb7b428.js","/_next/static/chunks/263f2cdcb9aa2341.js","/_next/static/chunks/294b9525248c8e5f.js"],"default"] 1d:T46e,Consideration is given to the control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The relationship between appropriately defined controllability, stabilizability properties, and the solution of the infinite time jump linear quadratic (JLQ) optimal control problems is also examined. Although the solution of the continuous-time Markov JLQ problem with finite or infinite time horizons is known, only sufficient conditions for the existence of finite cost, constant, stabilizing controls for the infinite time problem appear in the literature. In this paper necessary and sufficient conditions are established. These conditions are based on new definitions of controllability, observability, stabilizability, and detectability that are appropriate for continuous-time Markovian jump linear systems. These definitions play the same role for the JLQ problem as the deterministic properties do for the linear quadratic regulator (LQR) problem.< >1e:T437,Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/.< >1f:T41e,This note addresses the problem of H _infin filtering for continuous-time linear systems with Markovian jumping parameters. The main contribution of the note is to provide a method for designing an asymptotically stable linear time-invariant H _infin filter for systems where the jumping parameter is not accessible. The cases where the transition rate matrix of the Markov process is either exactly known, or unknown but belongs to a given polytope, are treated. The robust H _infin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a Lyapunov function that depends on the uncertain parameters is developed. The proposed filter designs are given in terms of linear matrix inequalities

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