Reachability, Controllability, Stabilisability, Observability

So far we've studied finite-horizon linear-quadratic optimal control problems. In this video lecture we introduce the concepts of reachabiliy, controllability, stabilisability and observability. These will be essential for the study of infinite-horizon LQ optimal control problems. In brief, a linear system is reachable if we can steer its state from ANY initial state to ANY target state in finite time by applying some sequence of control actions. A linear system is controllable if we can reach the ORIGIN from any initial state in finite time. A linear system is stabilisable if there is a linear controller that stabilises it. The matrix rank plays an important role in the study of these properties. ▬ Contents ▬▬▬▬▬▬▬▬▬▬ 00:00 - Introduction 00:40 - Rank 02:37 - Rank-Nullity Theorem 04:41 - Cayley-Hamilton Theorem 07:08 - Reachability 11:42 - Reachability example 12:55 - Controllability 13:20 - Controllability example 14:12 - Stabilisability 16:11 - Observability ▬ About ▬▬▬▬▬▬▬▬▬▬▬ This video is part of a series of video lectures for the module "Control Estimation Theory," which is taught in the MSc in Electronics, at the School of Electronics, Electrical Engineering and Computer Science (EEECS) at Queen's University Belfast (see https://www.qub.ac.uk/courses/postgraduate-taught/electronics-msc/). The module is taught by Dr Pantelis Sopasakis.