Exact Reconstruction of State and Disturbance for General Linear Systems Under Relaxed Conditions

This paper investigates the joint state and disturbance estimation for general linear multi-input multi-output (MIMO) systems that do not satisfy observer matching conditions. Resorting to invariant subspace decomposition, the given system is initially partitioned into two components: a strongly observable subsystem and a strongly detectable subsystem. For strongly observable subsystem, the step-to-step estimation scheme and prescribed-time differentiator are adopted to achieve accelerated state estimation. Cooperated with particular intermediate variables generated by decomposition algorithm, the influence of sluggish internal dynamics on the convergence rate of observers for strongly detectable subsystems is reduced. Moreover, the existence condition of the proposed observer is established. Instead of restrictive observer matching conditions, the proposed observer requires simply strong detectability and several common constraints on disturbance. Finally, three practical examples are provided to illustrate the effectiveness of the results.